Best Known (109−70, 109, s)-Nets in Base 27
(109−70, 109, 114)-Net over F27 — Constructive and digital
Digital (39, 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
(109−70, 109, 172)-Net in Base 27 — Constructive
(39, 109, 172)-net in base 27, using
- 271 times duplication [i] based on (38, 108, 172)-net in base 27, using
- t-expansion [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 81, 172)-net over F81, using
- t-expansion [i] based on (34, 108, 172)-net in base 27, using
(109−70, 109, 271)-Net over F27 — Digital
Digital (39, 109, 271)-net over F27, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(109−70, 109, 15326)-Net in Base 27 — Upper bound on s
There is no (39, 109, 15327)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 044753 509208 737004 035646 755934 617629 308835 394177 375706 695321 470629 123891 370775 913934 507431 334605 320759 960433 616499 306969 943214 606313 046606 613468 601944 077555 > 27109 [i]