Best Known (72, 96, s)-Nets in Base 3
(72, 96, 328)-Net over F3 — Constructive and digital
Digital (72, 96, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 24, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(72, 96, 501)-Net over F3 — Digital
Digital (72, 96, 501)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(396, 501, F3, 24) (dual of [501, 405, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(396, 728, F3, 24) (dual of [728, 632, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(396, 728, F3, 24) (dual of [728, 632, 25]-code), using
(72, 96, 17338)-Net in Base 3 — Upper bound on s
There is no (72, 96, 17339)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6364 524458 350624 386215 485925 330007 125989 506249 > 396 [i]