Best Known (64, 64+21, s)-Nets in Base 3
(64, 64+21, 328)-Net over F3 — Constructive and digital
Digital (64, 85, 328)-net over F3, using
- 31 times duplication [i] based on digital (63, 84, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 21, 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, 21, 82)-net over F81, using
(64, 64+21, 493)-Net over F3 — Digital
Digital (64, 85, 493)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(385, 493, F3, 21) (dual of [493, 408, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(385, 728, F3, 21) (dual of [728, 643, 22]-code), using
(64, 64+21, 23045)-Net in Base 3 — Upper bound on s
There is no (64, 85, 23046)-net in base 3, because
- 1 times m-reduction [i] would yield (64, 84, 23046)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 11975 180426 617429 634394 720401 395563 401981 > 384 [i]