Best Known (26, 64, s)-Nets in Base 27
(26, 64, 116)-Net over F27 — Constructive and digital
Digital (26, 64, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 42, 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 (3, 22, 52)-net over F27, using
(26, 64, 172)-Net in Base 27 — Constructive
(26, 64, 172)-net in base 27, using
- 12 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, 64, 208)-Net over F27 — Digital
Digital (26, 64, 208)-net over F27, using
- t-expansion [i] based on digital (24, 64, 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, 64, 244)-Net in Base 27
(26, 64, 244)-net in base 27, using
- 4 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, 64, 20205)-Net in Base 27 — Upper bound on s
There is no (26, 64, 20206)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 40 504008 523517 588207 237415 961139 215324 554224 479251 051454 125603 848747 353759 743264 160021 288305 > 2764 [i]