Best Known (61−39, 61, s)-Nets in Base 27
(61−39, 61, 112)-Net over F27 — Constructive and digital
Digital (22, 61, 112)-net over F27, using
- net from sequence [i] based on digital (22, 111)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 22 and N(F) ≥ 112, using
(61−39, 61, 160)-Net in Base 27 — Constructive
(22, 61, 160)-net in base 27, using
- 7 times m-reduction [i] based on (22, 68, 160)-net in base 27, using
- base change [i] based on digital (5, 51, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 51, 160)-net over F81, using
(61−39, 61, 163)-Net over F27 — Digital
Digital (22, 61, 163)-net over F27, using
- t-expansion [i] based on digital (21, 61, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
(61−39, 61, 190)-Net in Base 27
(22, 61, 190)-net in base 27, using
- 3 times m-reduction [i] based on (22, 64, 190)-net in base 27, using
- base change [i] based on digital (6, 48, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 48, 190)-net over F81, using
(61−39, 61, 10090)-Net in Base 27 — Upper bound on s
There is no (22, 61, 10091)-net in base 27, because
- 1 times m-reduction [i] would yield (22, 60, 10091)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 76 225509 539863 700361 240684 091469 514559 007779 736450 036732 256946 263421 151839 463226 660803 > 2760 [i]