Best Known (28, 28+12, s)-Nets in Base 5
(28, 28+12, 146)-Net over F5 — Constructive and digital
Digital (28, 40, 146)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 14)-net over F5, using
- digital (20, 32, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 16, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 16, 66)-net over F25, using
(28, 28+12, 596)-Net over F5 — Digital
Digital (28, 40, 596)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(540, 596, F5, 12) (dual of [596, 556, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(540, 624, F5, 12) (dual of [624, 584, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(540, 624, F5, 12) (dual of [624, 584, 13]-code), using
(28, 28+12, 34190)-Net in Base 5 — Upper bound on s
There is no (28, 40, 34191)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9095 008017 778034 200808 191465 > 540 [i]