Best Known (95, 95+13, s)-Nets in Base 5
(95, 95+13, 1398110)-Net over F5 — Constructive and digital
Digital (95, 108, 1398110)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-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 (1, 7, 10)-net over F5, using
(95, 95+13, 7727262)-Net over F5 — Digital
Digital (95, 108, 7727262)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5108, 7727262, F5, 13) (dual of [7727262, 7727154, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(5108, large, F5, 13) (dual of [large, large−108, 14]-code), using
- 7 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]
- 7 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(5108, large, F5, 13) (dual of [large, large−108, 14]-code), using
(95, 95+13, large)-Net in Base 5 — Upper bound on s
There is no (95, 108, large)-net in base 5, because
- 11 times m-reduction [i] would yield (95, 97, large)-net in base 5, but