Best Known (43−20, 43, s)-Nets in Base 25
(43−20, 43, 178)-Net over F25 — Constructive and digital
Digital (23, 43, 178)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 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, 30, 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, 13, 52)-net over F25, using
(43−20, 43, 567)-Net over F25 — Digital
Digital (23, 43, 567)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2543, 567, F25, 20) (dual of [567, 524, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2543, 639, F25, 20) (dual of [639, 596, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- 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(2529, 625, F25, 15) (dual of [625, 596, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2543, 639, F25, 20) (dual of [639, 596, 21]-code), using
(43−20, 43, 193595)-Net in Base 25 — Upper bound on s
There is no (23, 43, 193596)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1 292478 943224 254372 163171 567037 935745 677964 822185 048512 733121 > 2543 [i]