Best Known (30, 79, s)-Nets in Base 27
(30, 79, 114)-Net over F27 — Constructive and digital
Digital (30, 79, 114)-net over F27, using
- t-expansion [i] based on digital (23, 79, 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
(30, 79, 172)-Net in Base 27 — Constructive
(30, 79, 172)-net in base 27, using
- 13 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 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, 69, 172)-net over F81, using
(30, 79, 208)-Net over F27 — Digital
Digital (30, 79, 208)-net over F27, using
- t-expansion [i] based on digital (24, 79, 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
(30, 79, 244)-Net in Base 27
(30, 79, 244)-net in base 27, using
- 5 times m-reduction [i] based on (30, 84, 244)-net in base 27, using
- base change [i] based on digital (9, 63, 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, 63, 244)-net over F81, using
(30, 79, 16904)-Net in Base 27 — Upper bound on s
There is no (30, 79, 16905)-net in base 27, because
- 1 times m-reduction [i] would yield (30, 78, 16905)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 4432 762444 804547 994701 761403 122276 715042 683252 185977 428570 289491 374175 806003 086464 357448 962176 993184 852079 123361 > 2778 [i]