Best Known (90, 120, s)-Nets in Base 5
(90, 120, 408)-Net over F5 — Constructive and digital
Digital (90, 120, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 60, 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
(90, 120, 2620)-Net over F5 — Digital
Digital (90, 120, 2620)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5120, 2620, F5, 30) (dual of [2620, 2500, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
- 1 times truncation [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
(90, 120, 627276)-Net in Base 5 — Upper bound on s
There is no (90, 120, 627277)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 752319 563539 393613 976767 129839 348828 655856 089253 503750 141386 183570 330043 361254 237565 > 5120 [i]