Best Known (95, 127, s)-Nets in Base 5
(95, 127, 408)-Net over F5 — Constructive and digital
Digital (95, 127, 408)-net over F5, using
- 3 times m-reduction [i] based on digital (95, 130, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 65, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- trace code for nets [i] based on digital (30, 65, 204)-net over F25, using
(95, 127, 2576)-Net over F5 — Digital
Digital (95, 127, 2576)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5127, 2576, F5, 32) (dual of [2576, 2449, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 3131, F5, 32) (dual of [3131, 3004, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5126, 3130, F5, 32) (dual of [3130, 3004, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5126, 3130, F5, 32) (dual of [3130, 3004, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 3131, F5, 32) (dual of [3131, 3004, 33]-code), using
(95, 127, 600543)-Net in Base 5 — Upper bound on s
There is no (95, 127, 600544)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 58774 730352 150405 591694 066862 660685 843821 023474 136465 438219 740993 818403 916211 781560 246273 > 5127 [i]