Best Known (93−59, 93, s)-Nets in Base 27
(93−59, 93, 114)-Net over F27 — Constructive and digital
Digital (34, 93, 114)-net over F27, using
- t-expansion [i] based on digital (23, 93, 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
(93−59, 93, 172)-Net in Base 27 — Constructive
(34, 93, 172)-net in base 27, using
- 15 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 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, 81, 172)-net over F81, using
(93−59, 93, 220)-Net over F27 — Digital
Digital (34, 93, 220)-net over F27, using
- t-expansion [i] based on digital (33, 93, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
(93−59, 93, 244)-Net in Base 27
(34, 93, 244)-net in base 27, using
- 7 times m-reduction [i] based on (34, 100, 244)-net in base 27, using
- base change [i] based on digital (9, 75, 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, 75, 244)-net over F81, using
(93−59, 93, 15581)-Net in Base 27 — Upper bound on s
There is no (34, 93, 15582)-net in base 27, because
- 1 times m-reduction [i] would yield (34, 92, 15582)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 485254 850083 270855 278833 239058 901982 664327 971866 555587 654649 895521 864060 785949 053872 713627 937617 500800 996215 691823 591626 537111 284725 > 2792 [i]