Best Known (94−59, 94, s)-Nets in Base 27
(94−59, 94, 114)-Net over F27 — Constructive and digital
Digital (35, 94, 114)-net over F27, using
- t-expansion [i] based on digital (23, 94, 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
(94−59, 94, 172)-Net in Base 27 — Constructive
(35, 94, 172)-net in base 27, using
- t-expansion [i] based on (34, 94, 172)-net in base 27, using
- 14 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
- 14 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
(94−59, 94, 220)-Net over F27 — Digital
Digital (35, 94, 220)-net over F27, using
- t-expansion [i] based on digital (33, 94, 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
(94−59, 94, 244)-Net in Base 27
(35, 94, 244)-net in base 27, using
- 10 times m-reduction [i] based on (35, 104, 244)-net in base 27, using
- base change [i] based on digital (9, 78, 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, 78, 244)-net over F81, using
(94−59, 94, 17458)-Net in Base 27 — Upper bound on s
There is no (35, 94, 17459)-net in base 27, because
- 1 times m-reduction [i] would yield (35, 93, 17459)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 13 096249 276254 346155 453348 645379 777712 078531 904162 855912 553225 183168 807219 747221 262794 067897 196349 117121 807920 621185 857960 262418 621975 > 2793 [i]