Best Known (44−23, 44, s)-Nets in Base 25
(44−23, 44, 152)-Net over F25 — Constructive and digital
Digital (21, 44, 152)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-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 (0, 11, 26)-net over F25, using
(44−23, 44, 255)-Net over F25 — Digital
Digital (21, 44, 255)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2544, 255, F25, 23) (dual of [255, 211, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2544, 312, F25, 23) (dual of [312, 268, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2544, 312, F25, 23) (dual of [312, 268, 24]-code), using
(44−23, 44, 59626)-Net in Base 25 — Upper bound on s
There is no (21, 44, 59627)-net in base 25, because
- 1 times m-reduction [i] would yield (21, 43, 59627)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 292640 557934 671007 830288 819377 227672 469969 610430 402183 576025 > 2543 [i]