Best Known (26, 26+37, s)-Nets in Base 27
(26, 26+37, 128)-Net over F27 — Constructive and digital
Digital (26, 63, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 41, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 22, 64)-net over F27, using
(26, 26+37, 172)-Net in Base 27 — Constructive
(26, 63, 172)-net in base 27, using
- 13 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
(26, 26+37, 208)-Net over F27 — Digital
Digital (26, 63, 208)-net over F27, using
- t-expansion [i] based on digital (24, 63, 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
(26, 26+37, 244)-Net in Base 27
(26, 63, 244)-net in base 27, using
- 5 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
(26, 26+37, 24731)-Net in Base 27 — Upper bound on s
There is no (26, 63, 24732)-net in base 27, because
- 1 times m-reduction [i] would yield (26, 62, 24732)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 55558 465569 463228 084559 611329 434185 865269 053120 289885 259312 809180 687309 087252 413778 242505 > 2762 [i]