Best Known (31, 31+77, s)-Nets in Base 27
(31, 31+77, 114)-Net over F27 — Constructive and digital
Digital (31, 108, 114)-net over F27, using
- t-expansion [i] based on digital (23, 108, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(31, 31+77, 150)-Net in Base 27 — Constructive
(31, 108, 150)-net in base 27, using
- base change [i] based on digital (4, 81, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
(31, 31+77, 208)-Net over F27 — Digital
Digital (31, 108, 208)-net over F27, using
- t-expansion [i] based on digital (24, 108, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(31, 31+77, 6178)-Net in Base 27 — Upper bound on s
There is no (31, 108, 6179)-net in base 27, because
- 1 times m-reduction [i] would yield (31, 107, 6179)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1440 617496 267133 700310 111290 430711 904090 954860 319909 188725 072222 773482 999387 988010 252715 585004 622968 604302 431859 211323 497712 136685 849459 654063 689767 122573 > 27107 [i]