Best Known (30−12, 30, s)-Nets in Base 5
(30−12, 30, 104)-Net over F5 — Constructive and digital
Digital (18, 30, 104)-net over F5, using
- trace code for nets [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
(30−12, 30, 115)-Net over F5 — Digital
Digital (18, 30, 115)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(530, 115, F5, 12) (dual of [115, 85, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(530, 124, F5, 12) (dual of [124, 94, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(530, 124, F5, 12) (dual of [124, 94, 13]-code), using
(30−12, 30, 2334)-Net in Base 5 — Upper bound on s
There is no (18, 30, 2335)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 931 549328 402238 856169 > 530 [i]