Best Known (109−78, 109, s)-Nets in Base 27
(109−78, 109, 114)-Net over F27 — Constructive and digital
Digital (31, 109, 114)-net over F27, using
- t-expansion [i] based on digital (23, 109, 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
(109−78, 109, 116)-Net in Base 27 — Constructive
(31, 109, 116)-net in base 27, using
- 271 times duplication [i] based on (30, 108, 116)-net in base 27, using
- t-expansion [i] based on (29, 108, 116)-net in base 27, using
- base change [i] based on digital (2, 81, 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
- base change [i] based on digital (2, 81, 116)-net over F81, using
- t-expansion [i] based on (29, 108, 116)-net in base 27, using
(109−78, 109, 208)-Net over F27 — Digital
Digital (31, 109, 208)-net over F27, using
- t-expansion [i] based on digital (24, 109, 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
(109−78, 109, 5907)-Net in Base 27 — Upper bound on s
There is no (31, 109, 5908)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 045150 629929 523448 035174 687125 403793 134808 885065 977475 982612 954794 211405 631396 365417 062508 235986 438519 871236 061964 949695 083863 773849 222243 991860 077068 116881 > 27109 [i]