Best Known (36, 36+55, s)-Nets in Base 27
(36, 36+55, 132)-Net over F27 — Constructive and digital
Digital (36, 91, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 31, 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, 60, 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, 31, 64)-net over F27, using
(36, 36+55, 224)-Net in Base 27 — Constructive
(36, 91, 224)-net in base 27, using
- 1 times m-reduction [i] based on (36, 92, 224)-net in base 27, using
- base change [i] based on digital (13, 69, 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, 69, 224)-net over F81, using
(36, 36+55, 244)-Net over F27 — Digital
Digital (36, 91, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
(36, 36+55, 298)-Net in Base 27
(36, 91, 298)-net in base 27, using
- 5 times m-reduction [i] based on (36, 96, 298)-net in base 27, using
- base change [i] based on digital (12, 72, 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, 72, 298)-net over F81, using
(36, 36+55, 24797)-Net in Base 27 — Upper bound on s
There is no (36, 91, 24798)-net in base 27, because
- 1 times m-reduction [i] would yield (36, 90, 24798)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 665 553226 966355 539730 566811 572079 759476 440083 606407 216919 435832 625307 895753 442406 839546 449334 044790 093692 530967 600898 278488 677089 > 2790 [i]