Best Known (36, 36+53, s)-Nets in Base 27
(36, 36+53, 140)-Net over F27 — Constructive and digital
Digital (36, 89, 140)-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 (6, 59, 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 (4, 30, 64)-net over F27, using
(36, 36+53, 224)-Net in Base 27 — Constructive
(36, 89, 224)-net in base 27, using
- 3 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+53, 244)-Net over F27 — Digital
Digital (36, 89, 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+53, 298)-Net in Base 27
(36, 89, 298)-net in base 27, using
- 7 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+53, 28361)-Net in Base 27 — Upper bound on s
There is no (36, 89, 28362)-net in base 27, because
- 1 times m-reduction [i] would yield (36, 88, 28362)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 912470 934342 920551 346277 955169 537303 745909 497854 601205 601446 298937 175688 054160 672893 240096 733816 695528 463334 472960 767957 485493 > 2788 [i]