Best Known (44−31, 44, s)-Nets in Base 27
(44−31, 44, 96)-Net over F27 — Constructive and digital
Digital (13, 44, 96)-net over F27, using
- t-expansion [i] based on digital (11, 44, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(44−31, 44, 116)-Net in Base 27 — Constructive
(13, 44, 116)-net in base 27, using
- base change [i] based on digital (2, 33, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
(44−31, 44, 136)-Net over F27 — Digital
Digital (13, 44, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(44−31, 44, 3125)-Net in Base 27 — Upper bound on s
There is no (13, 44, 3126)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 43, 3126)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 35 375048 319394 464668 274725 280388 426610 793178 662593 630279 802393 > 2743 [i]