Best Known (88−54, 88, s)-Nets in Base 27
(88−54, 88, 116)-Net over F27 — Constructive and digital
Digital (34, 88, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 30, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 58, 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 (3, 30, 52)-net over F27, using
(88−54, 88, 172)-Net in Base 27 — Constructive
(34, 88, 172)-net in base 27, using
- 20 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
(88−54, 88, 220)-Net over F27 — Digital
Digital (34, 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
(88−54, 88, 298)-Net in Base 27
(34, 88, 298)-net in base 27, using
- base change [i] based on digital (12, 66, 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
(88−54, 88, 19422)-Net in Base 27 — Upper bound on s
There is no (34, 88, 19423)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 912659 474918 644092 793931 742739 546153 400961 593450 105094 105796 908306 348416 665372 097291 048593 812370 957864 703685 309579 422511 150019 > 2788 [i]