Best Known (23, 49, s)-Nets in Base 25
(23, 49, 152)-Net over F25 — Constructive and digital
Digital (23, 49, 152)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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, 36, 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, 13, 26)-net over F25, using
(23, 49, 271)-Net over F25 — Digital
Digital (23, 49, 271)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2549, 271, F25, 2, 26) (dual of [(271, 2), 493, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2549, 312, F25, 2, 26) (dual of [(312, 2), 575, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2549, 624, F25, 26) (dual of [624, 575, 27]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- OOA 2-folding [i] based on linear OA(2549, 624, F25, 26) (dual of [624, 575, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(2549, 312, F25, 2, 26) (dual of [(312, 2), 575, 27]-NRT-code), using
(23, 49, 43882)-Net in Base 25 — Upper bound on s
There is no (23, 49, 43883)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 315 616273 651525 283147 978316 540318 974749 723097 544962 350688 966152 587625 > 2549 [i]