Best Known (74, 74+24, s)-Nets in Base 5
(74, 74+24, 400)-Net over F5 — Constructive and digital
Digital (74, 98, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 49, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(74, 74+24, 2718)-Net over F5 — Digital
Digital (74, 98, 2718)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(598, 2718, F5, 24) (dual of [2718, 2620, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(598, 3138, F5, 24) (dual of [3138, 3040, 25]-code), using
- construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- linear OA(596, 3125, F5, 24) (dual of [3125, 3029, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(586, 3125, F5, 22) (dual of [3125, 3039, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(581, 3125, F5, 21) (dual of [3125, 3044, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(51, 12, F5, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(598, 3138, F5, 24) (dual of [3138, 3040, 25]-code), using
(74, 74+24, 675384)-Net in Base 5 — Upper bound on s
There is no (74, 98, 675385)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 315 548014 240317 678148 836919 662590 040992 189450 007552 348417 307507 238225 > 598 [i]