Best Known (88−53, 88, s)-Nets in Base 27
(88−53, 88, 132)-Net over F27 — Constructive and digital
Digital (35, 88, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 30, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (5, 58, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 30, 64)-net over F27, using
(88−53, 88, 220)-Net over F27 — Digital
Digital (35, 88, 220)-net over F27, using
- t-expansion [i] based on digital (33, 88, 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
(88−53, 88, 224)-Net in Base 27 — Constructive
(35, 88, 224)-net in base 27, using
- base change [i] based on digital (13, 66, 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
(88−53, 88, 298)-Net in Base 27
(35, 88, 298)-net in base 27, using
- 4 times m-reduction [i] based on (35, 92, 298)-net in base 27, using
- base change [i] based on digital (12, 69, 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, 69, 298)-net over F81, using
(88−53, 88, 24983)-Net in Base 27 — Upper bound on s
There is no (35, 88, 24984)-net in base 27, because
- 1 times m-reduction [i] would yield (35, 87, 24984)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 33806 349816 320977 320763 577452 173635 369433 388069 416556 553938 425577 193222 887296 289920 619509 915602 306915 702957 214421 269241 360785 > 2787 [i]