Best Known (48−24, 48, s)-Nets in Base 25
(48−24, 48, 156)-Net over F25 — Constructive and digital
Digital (24, 48, 156)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 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, 33, 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, 15, 52)-net over F25, using
(48−24, 48, 356)-Net over F25 — Digital
Digital (24, 48, 356)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2548, 356, F25, 24) (dual of [356, 308, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2548, 630, F25, 24) (dual of [630, 582, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(2547, 625, F25, 24) (dual of [625, 578, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2548, 630, F25, 24) (dual of [630, 582, 25]-code), using
(48−24, 48, 86075)-Net in Base 25 — Upper bound on s
There is no (24, 48, 86076)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 12 622521 367198 463930 693447 107032 294595 552210 354208 651783 336649 105025 > 2548 [i]