Best Known (67−34, 67, s)-Nets in Base 27
(67−34, 67, 170)-Net over F27 — Constructive and digital
Digital (33, 67, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 24, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (9, 43, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (7, 24, 82)-net over F27, using
(67−34, 67, 370)-Net in Base 27 — Constructive
(33, 67, 370)-net in base 27, using
- 1 times m-reduction [i] based on (33, 68, 370)-net in base 27, using
- base change [i] based on digital (16, 51, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 51, 370)-net over F81, using
(67−34, 67, 427)-Net over F27 — Digital
Digital (33, 67, 427)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2767, 427, F27, 34) (dual of [427, 360, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2767, 728, F27, 34) (dual of [728, 661, 35]-code), using
(67−34, 67, 120836)-Net in Base 27 — Upper bound on s
There is no (33, 67, 120837)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 796903 989109 515599 131785 351665 191552 020884 572480 493807 755012 928772 661305 258372 800065 456302 169539 > 2767 [i]