Best Known (47−23, 47, s)-Nets in Base 25
(47−23, 47, 178)-Net over F25 — Constructive and digital
Digital (24, 47, 178)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (10, 33, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (3, 14, 52)-net over F25, using
(47−23, 47, 408)-Net over F25 — Digital
Digital (24, 47, 408)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2547, 408, F25, 23) (dual of [408, 361, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2547, 633, F25, 23) (dual of [633, 586, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(2545, 625, F25, 23) (dual of [625, 580, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2539, 625, F25, 20) (dual of [625, 586, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2547, 633, F25, 23) (dual of [633, 586, 24]-code), using
(47−23, 47, 143455)-Net in Base 25 — Upper bound on s
There is no (24, 47, 143456)-net in base 25, because
- 1 times m-reduction [i] would yield (24, 46, 143456)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 20195 545718 048340 568092 565120 927914 870525 761395 216554 206541 076225 > 2546 [i]