Best Known (75−46, 75, s)-Nets in Base 27
(75−46, 75, 114)-Net over F27 — Constructive and digital
Digital (29, 75, 114)-net over F27, using
- t-expansion [i] based on digital (23, 75, 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
(75−46, 75, 172)-Net in Base 27 — Constructive
(29, 75, 172)-net in base 27, using
- 13 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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, 66, 172)-net over F81, using
(75−46, 75, 208)-Net over F27 — Digital
Digital (29, 75, 208)-net over F27, using
- t-expansion [i] based on digital (24, 75, 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
(75−46, 75, 244)-Net in Base 27
(29, 75, 244)-net in base 27, using
- 5 times m-reduction [i] based on (29, 80, 244)-net in base 27, using
- base change [i] based on digital (9, 60, 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, 60, 244)-net over F81, using
(75−46, 75, 16852)-Net in Base 27 — Upper bound on s
There is no (29, 75, 16853)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 225169 236163 665133 161351 839108 273001 146463 361491 773921 794907 965370 657500 982531 797748 987502 198540 169399 825443 > 2775 [i]