Best Known (21, 41, s)-Nets in Base 25
(21, 41, 153)-Net over F25 — Constructive and digital
Digital (21, 41, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-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 (1, 11, 27)-net over F25, using
(21, 41, 394)-Net over F25 — Digital
Digital (21, 41, 394)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2541, 394, F25, 20) (dual of [394, 353, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, 633, F25, 20) (dual of [633, 592, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [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(2533, 625, F25, 17) (dual of [625, 592, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(2541, 633, F25, 20) (dual of [633, 592, 21]-code), using
(21, 41, 101694)-Net in Base 25 — Upper bound on s
There is no (21, 41, 101695)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2068 022941 586563 032324 460770 228512 296495 733865 917749 895953 > 2541 [i]