Best Known (90−58, 90, s)-Nets in Base 27
(90−58, 90, 114)-Net over F27 — Constructive and digital
Digital (32, 90, 114)-net over F27, using
- t-expansion [i] based on digital (23, 90, 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
(90−58, 90, 172)-Net in Base 27 — Constructive
(32, 90, 172)-net in base 27, using
- 10 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
(90−58, 90, 208)-Net over F27 — Digital
Digital (32, 90, 208)-net over F27, using
- t-expansion [i] based on digital (24, 90, 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
(90−58, 90, 244)-Net in Base 27
(32, 90, 244)-net in base 27, using
- 2 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
(90−58, 90, 12410)-Net in Base 27 — Upper bound on s
There is no (32, 90, 12411)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 665 901775 101613 785576 323068 756259 487466 580408 473354 498411 553539 596735 650663 676949 457935 876164 314366 259713 836779 832270 709210 939943 > 2790 [i]