Best Known (94−55, 94, s)-Nets in Base 27
(94−55, 94, 152)-Net over F27 — Constructive and digital
Digital (39, 94, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 33, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 61, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 33, 76)-net over F27, using
(94−55, 94, 224)-Net in Base 27 — Constructive
(39, 94, 224)-net in base 27, using
- 10 times m-reduction [i] based on (39, 104, 224)-net in base 27, using
- base change [i] based on digital (13, 78, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 78, 224)-net over F81, using
(94−55, 94, 271)-Net over F27 — Digital
Digital (39, 94, 271)-net over F27, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(94−55, 94, 298)-Net in Base 27
(39, 94, 298)-net in base 27, using
- 14 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
(94−55, 94, 35769)-Net in Base 27 — Upper bound on s
There is no (39, 94, 35770)-net in base 27, because
- 1 times m-reduction [i] would yield (39, 93, 35770)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 13 089097 444407 818273 908119 552707 249813 031065 068345 232498 748123 616911 561595 034481 871322 643804 084822 445379 410850 733811 038467 398073 622257 > 2793 [i]