Best Known (38−6, 38, s)-Nets in Base 49
(38−6, 38, large)-Net over F49 — Constructive and digital
Digital (32, 38, large)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (29, 35, 8388602)-net over F49, using
- net defined by OOA [i] based on linear OOA(4935, 8388602, F49, 9, 6) (dual of [(8388602, 9), 75497383, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(4935, large, F49, 3, 6), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(490, s, F49, 3, 0) with arbitrarily large s, using
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code) (see above)
- linear OOA(491, 120100, F49, 3, 1) (dual of [(120100, 3), 360299, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(491, s, F49, 3, 1) with arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(491, s, F49, 3, 1) with arbitrarily large s, using
- linear OOA(491, 120100, F49, 3, 1) (dual of [(120100, 3), 360299, 2]-NRT-code) (see above)
- linear OOA(491, 120100, F49, 3, 1) (dual of [(120100, 3), 360299, 2]-NRT-code) (see above)
- linear OOA(494, 120100, F49, 3, 2) (dual of [(120100, 3), 360296, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(494, 120100, F49, 2, 2) (dual of [(120100, 2), 240196, 3]-NRT-code), using
- appending kth column [i] based on linear OA(494, 120100, F49, 2) (dual of [120100, 120096, 3]-code), using
- Hamming code H(4,49) [i]
- appending kth column [i] based on linear OA(494, 120100, F49, 2) (dual of [120100, 120096, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(494, 120100, F49, 2, 2) (dual of [(120100, 2), 240196, 3]-NRT-code), using
- linear OOA(497, 1921601, F49, 3, 3) (dual of [(1921601, 3), 5764796, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(497, 5769602, F49, 3, 3) (dual of [(5769602, 3), 17308799, 4]-NRT-code), using
- linear OOA(4921, 1921601, F49, 3, 6) (dual of [(1921601, 3), 5764782, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- OOA 3-folding [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- linear OOA(490, 120100, F49, 3, 0) (dual of [(120100, 3), 360300, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(4935, large, F49, 3, 6), using
- net defined by OOA [i] based on linear OOA(4935, 8388602, F49, 9, 6) (dual of [(8388602, 9), 75497383, 7]-NRT-code), using
- digital (0, 3, 50)-net over F49, using
(38−6, 38, large)-Net in Base 49 — Upper bound on s
There is no (32, 38, large)-net in base 49, because
- 4 times m-reduction [i] would yield (32, 34, large)-net in base 49, but