Best Known (94, 94+13, s)-Nets in Base 5
(94, 94+13, 1398106)-Net over F5 — Constructive and digital
Digital (94, 107, 1398106)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- digital (88, 101, 1398100)-net over F5, using
- net defined by OOA [i] based on linear OOA(5101, 1398100, F5, 13, 13) (dual of [(1398100, 13), 18175199, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(5101, 8388601, F5, 13) (dual of [8388601, 8388500, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(5101, 8388601, F5, 13) (dual of [8388601, 8388500, 14]-code), using
- net defined by OOA [i] based on linear OOA(5101, 1398100, F5, 13, 13) (dual of [(1398100, 13), 18175199, 14]-NRT-code), using
- digital (0, 6, 6)-net over F5, using
(94, 94+13, 6675485)-Net over F5 — Digital
Digital (94, 107, 6675485)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5107, 6675485, F5, 13) (dual of [6675485, 6675378, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(5107, large, F5, 13) (dual of [large, large−107, 14]-code), using
- 6 times code embedding in larger space [i] based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 6 times code embedding in larger space [i] based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(5107, large, F5, 13) (dual of [large, large−107, 14]-code), using
(94, 94+13, large)-Net in Base 5 — Upper bound on s
There is no (94, 107, large)-net in base 5, because
- 11 times m-reduction [i] would yield (94, 96, large)-net in base 5, but