Best Known (95, 126, s)-Nets in Base 3
(95, 126, 328)-Net over F3 — Constructive and digital
Digital (95, 126, 328)-net over F3, using
- 32 times duplication [i] based on digital (93, 124, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 31, 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
- trace code for nets [i] based on digital (0, 31, 82)-net over F81, using
(95, 126, 639)-Net over F3 — Digital
Digital (95, 126, 639)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3126, 639, F3, 31) (dual of [639, 513, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3126, 747, F3, 31) (dual of [747, 621, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- linear OA(3121, 730, F3, 31) (dual of [730, 609, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3109, 730, F3, 27) (dual of [730, 621, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(35, 17, F3, 3) (dual of [17, 12, 4]-code or 17-cap in PG(4,3)), using
- construction X applied to C([0,15]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3126, 747, F3, 31) (dual of [747, 621, 32]-code), using
(95, 126, 30376)-Net in Base 3 — Upper bound on s
There is no (95, 126, 30377)-net in base 3, because
- 1 times m-reduction [i] would yield (95, 125, 30377)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 436748 816534 052013 104218 746669 176286 715875 388620 483727 055627 > 3125 [i]