Best Known (13, 19, s)-Nets in Base 81
(13, 19, 177230)-Net over F81 — Constructive and digital
Digital (13, 19, 177230)-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 (10, 16, 177148)-net over F81, using
- net defined by OOA [i] based on linear OOA(8116, 177148, F81, 6, 6) (dual of [(177148, 6), 1062872, 7]-NRT-code), using
- OA 3-folding and stacking [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
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- net defined by OOA [i] based on linear OOA(8116, 177148, F81, 6, 6) (dual of [(177148, 6), 1062872, 7]-NRT-code), using
- digital (0, 3, 82)-net over F81, using
(13, 19, 582091)-Net over F81 — Digital
Digital (13, 19, 582091)-net over F81, using
(13, 19, large)-Net in Base 81 — Upper bound on s
There is no (13, 19, large)-net in base 81, because
- 4 times m-reduction [i] would yield (13, 15, large)-net in base 81, but