Best Known (101−61, 101, s)-Nets in Base 27
(101−61, 101, 140)-Net over F27 — Constructive and digital
Digital (40, 101, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 34, 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, 67, 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, 34, 64)-net over F27, using
(101−61, 101, 224)-Net in Base 27 — Constructive
(40, 101, 224)-net in base 27, using
- 7 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 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, 81, 224)-net over F81, using
(101−61, 101, 273)-Net over F27 — Digital
Digital (40, 101, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
(101−61, 101, 298)-Net in Base 27
(40, 101, 298)-net in base 27, using
- t-expansion [i] based on (39, 101, 298)-net in base 27, using
- 7 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
- 7 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(101−61, 101, 27338)-Net in Base 27 — Upper bound on s
There is no (40, 101, 27339)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 100, 27339)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 136922 907718 468966 077313 621508 847216 839491 480214 319413 793910 946506 903510 268678 509070 504069 693527 082821 475702 778620 479719 418327 935088 179043 911085 > 27100 [i]