Best Known (89−57, 89, s)-Nets in Base 27
(89−57, 89, 114)-Net over F27 — Constructive and digital
Digital (32, 89, 114)-net over F27, using
- t-expansion [i] based on digital (23, 89, 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
(89−57, 89, 172)-Net in Base 27 — Constructive
(32, 89, 172)-net in base 27, using
- 11 times m-reduction [i] based on (32, 100, 172)-net in base 27, using
- base change [i] based on digital (7, 75, 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, 75, 172)-net over F81, using
(89−57, 89, 208)-Net over F27 — Digital
Digital (32, 89, 208)-net over F27, using
- t-expansion [i] based on digital (24, 89, 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
(89−57, 89, 244)-Net in Base 27
(32, 89, 244)-net in base 27, using
- 3 times m-reduction [i] based on (32, 92, 244)-net in base 27, using
- base change [i] based on digital (9, 69, 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, 69, 244)-net over F81, using
(89−57, 89, 13681)-Net in Base 27 — Upper bound on s
There is no (32, 89, 13682)-net in base 27, because
- 1 times m-reduction [i] would yield (32, 88, 13682)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 912529 628780 572455 079491 016787 150991 357107 557654 778760 385967 446371 412177 296697 192451 954447 959506 284423 899166 237146 353177 103385 > 2788 [i]