Best Known (45−22, 45, s)-Nets in Base 25
(45−22, 45, 156)-Net over F25 — Constructive and digital
Digital (23, 45, 156)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 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, 31, 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, 14, 52)-net over F25, using
(45−22, 45, 403)-Net over F25 — Digital
Digital (23, 45, 403)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2545, 403, F25, 22) (dual of [403, 358, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2545, 633, F25, 22) (dual of [633, 588, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(2543, 625, F25, 22) (dual of [625, 582, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2537, 625, F25, 19) (dual of [625, 588, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2545, 633, F25, 22) (dual of [633, 588, 23]-code), using
(45−22, 45, 107059)-Net in Base 25 — Upper bound on s
There is no (23, 45, 107060)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 807 813530 609496 388224 943791 723434 503499 211750 878094 910786 108705 > 2545 [i]