Best Known (27, 39, s)-Nets in Base 3
(27, 39, 114)-Net over F3 — Constructive and digital
Digital (27, 39, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 13, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
(27, 39, 139)-Net over F3 — Digital
Digital (27, 39, 139)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(339, 139, F3, 12) (dual of [139, 100, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(339, 161, F3, 12) (dual of [161, 122, 13]-code), using
- 1 times truncation [i] based on linear OA(340, 162, F3, 13) (dual of [162, 122, 14]-code), using
- a “GraB†code from Grassl’s database [i]
- 1 times truncation [i] based on linear OA(340, 162, F3, 13) (dual of [162, 122, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(339, 161, F3, 12) (dual of [161, 122, 13]-code), using
(27, 39, 1884)-Net in Base 3 — Upper bound on s
There is no (27, 39, 1885)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4 057871 719789 909425 > 339 [i]