Best Known (100−61, 100, s)-Nets in Base 27
(100−61, 100, 132)-Net over F27 — Constructive and digital
Digital (39, 100, 132)-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 (5, 66, 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, 34, 64)-net over F27, using
(100−61, 100, 224)-Net in Base 27 — Constructive
(39, 100, 224)-net in base 27, using
- 4 times m-reduction [i] based on (39, 104, 224)-net in base 27, using
- base change [i] based on digital (13, 78, 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, 78, 224)-net over F81, using
(100−61, 100, 271)-Net over F27 — Digital
Digital (39, 100, 271)-net over F27, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(100−61, 100, 298)-Net in Base 27
(39, 100, 298)-net in base 27, using
- 8 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
(100−61, 100, 24492)-Net in Base 27 — Upper bound on s
There is no (39, 100, 24493)-net in base 27, because
- 1 times m-reduction [i] would yield (39, 99, 24493)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 5071 342181 999568 995950 381244 475050 547492 506369 774500 112378 637233 344881 287313 922378 547634 240805 164032 179783 392930 751722 174452 334091 028452 374625 > 2799 [i]