Best Known (43−21, 43, s)-Nets in Base 25
(43−21, 43, 156)-Net over F25 — Constructive and digital
Digital (22, 43, 156)-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 (9, 30, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (3, 13, 52)-net over F25, using
(43−21, 43, 398)-Net over F25 — Digital
Digital (22, 43, 398)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2543, 398, F25, 21) (dual of [398, 355, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2543, 633, F25, 21) (dual of [633, 590, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(2541, 625, F25, 21) (dual of [625, 584, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2535, 625, F25, 18) (dual of [625, 590, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2543, 633, F25, 21) (dual of [633, 590, 22]-code), using
(43−21, 43, 140312)-Net in Base 25 — Upper bound on s
There is no (22, 43, 140313)-net in base 25, because
- 1 times m-reduction [i] would yield (22, 42, 140313)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 51698 823835 091321 991909 928573 748819 410884 545034 757738 549681 > 2542 [i]