Best Known (26, 26+4, s)-Nets in Base 81
(26, 26+4, large)-Net over F81 — Constructive and digital
Digital (26, 30, large)-net over F81, using
- 2 times m-reduction [i] based on digital (26, 32, large)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- digital (23, 29, 8388602)-net over F81, using
- net defined by OOA [i] based on linear OOA(8129, 8388602, F81, 9, 6) (dual of [(8388602, 9), 75497389, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8129, large, F81, 3, 6), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(810, s, F81, 3, 0) with arbitrarily large s, using
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code) (see above)
- linear OOA(811, 177148, F81, 3, 1) (dual of [(177148, 3), 531443, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) with arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) with arbitrarily large s, using
- linear OOA(811, 177148, F81, 3, 1) (dual of [(177148, 3), 531443, 2]-NRT-code) (see above)
- linear OOA(811, 177148, F81, 3, 1) (dual of [(177148, 3), 531443, 2]-NRT-code) (see above)
- linear OOA(814, 177148, F81, 3, 2) (dual of [(177148, 3), 531440, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 3, 2) (dual of [(538084, 3), 1614248, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(814, 538084, F81, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
- appending kth column [i] based on linear OA(814, 538084, F81, 2) (dual of [538084, 538080, 3]-code), using
- Hamming code H(4,81) [i]
- appending kth column [i] based on linear OA(814, 538084, F81, 2) (dual of [538084, 538080, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(814, 538084, F81, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 3, 2) (dual of [(538084, 3), 1614248, 3]-NRT-code), using
- linear OOA(816, 177148, F81, 3, 3) (dual of [(177148, 3), 531438, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(816, 538247, F81, 3, 3) (dual of [(538247, 3), 1614735, 4]-NRT-code), using
- linear OOA(8116, 177148, F81, 3, 6) (dual of [(177148, 3), 531428, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OOA 3-folding [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- linear OOA(810, 177148, F81, 3, 0) (dual of [(177148, 3), 531444, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(8129, large, F81, 3, 6), using
- net defined by OOA [i] based on linear OOA(8129, 8388602, F81, 9, 6) (dual of [(8388602, 9), 75497389, 7]-NRT-code), using
- digital (0, 3, 82)-net over F81, using
- (u, u+v)-construction [i] based on
(26, 26+4, large)-Net in Base 81 — Upper bound on s
There is no (26, 30, large)-net in base 81, because
- 2 times m-reduction [i] would yield (26, 28, large)-net in base 81, but