Best Known (18, 31, s)-Nets in Base 5
(18, 31, 56)-Net over F5 — Constructive and digital
Digital (18, 31, 56)-net over F5, using
- 1 times m-reduction [i] based on digital (18, 32, 56)-net over F5, using
- trace code for nets [i] based on digital (2, 16, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- trace code for nets [i] based on digital (2, 16, 28)-net over F25, using
(18, 31, 93)-Net over F5 — Digital
Digital (18, 31, 93)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(531, 93, F5, 13) (dual of [93, 62, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(531, 124, F5, 13) (dual of [124, 93, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(531, 124, F5, 13) (dual of [124, 93, 14]-code), using
(18, 31, 2334)-Net in Base 5 — Upper bound on s
There is no (18, 31, 2335)-net in base 5, because
- 1 times m-reduction [i] would yield (18, 30, 2335)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 931 549328 402238 856169 > 530 [i]