Best Known (66−40, 66, s)-Nets in Base 27
(66−40, 66, 114)-Net over F27 — Constructive and digital
Digital (26, 66, 114)-net over F27, using
- t-expansion [i] based on digital (23, 66, 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
(66−40, 66, 172)-Net in Base 27 — Constructive
(26, 66, 172)-net in base 27, using
- 10 times m-reduction [i] based on (26, 76, 172)-net in base 27, using
- base change [i] based on digital (7, 57, 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, 57, 172)-net over F81, using
(66−40, 66, 208)-Net over F27 — Digital
Digital (26, 66, 208)-net over F27, using
- t-expansion [i] based on digital (24, 66, 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
(66−40, 66, 244)-Net in Base 27
(26, 66, 244)-net in base 27, using
- 2 times m-reduction [i] based on (26, 68, 244)-net in base 27, using
- base change [i] based on digital (9, 51, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 51, 244)-net over F81, using
(66−40, 66, 16887)-Net in Base 27 — Upper bound on s
There is no (26, 66, 16888)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 29524 741927 323143 755585 905257 535830 062320 395695 231328 413905 188740 559755 543929 652529 829192 924609 > 2766 [i]