Best Known (105, 141, s)-Nets in Base 5
(105, 141, 410)-Net over F5 — Constructive and digital
Digital (105, 141, 410)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 19, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (86, 122, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 61, 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
- trace code for nets [i] based on digital (25, 61, 200)-net over F25, using
- digital (1, 19, 10)-net over F5, using
(105, 141, 2532)-Net over F5 — Digital
Digital (105, 141, 2532)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5141, 2532, F5, 36) (dual of [2532, 2391, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using
(105, 141, 564059)-Net in Base 5 — Upper bound on s
There is no (105, 141, 564060)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 358 735571 103974 995413 687234 622849 236663 959498 545264 411569 974696 667241 901156 584552 408416 913732 958785 > 5141 [i]