Best Known (23, 23+27, s)-Nets in Base 25
(23, 23+27, 152)-Net over F25 — Constructive and digital
Digital (23, 50, 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, 37, 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, 23+27, 244)-Net over F25 — Digital
Digital (23, 50, 244)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2550, 244, F25, 2, 27) (dual of [(244, 2), 438, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2550, 313, F25, 2, 27) (dual of [(313, 2), 576, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2550, 626, F25, 27) (dual of [626, 576, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(2550, 625, F25, 27) (dual of [625, 575, 28]-code), using an extension Ce(26) of 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]
- linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(250, 1, F25, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(2550, 626, F25, 27) (dual of [626, 576, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2550, 313, F25, 2, 27) (dual of [(313, 2), 576, 28]-NRT-code), using
(23, 23+27, 43882)-Net in Base 25 — Upper bound on s
There is no (23, 50, 43883)-net in base 25, because
- 1 times m-reduction [i] would yield (23, 49, 43883)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 315 616273 651525 283147 978316 540318 974749 723097 544962 350688 966152 587625 > 2549 [i]