Best Known (22, 49, s)-Nets in Base 27
(22, 49, 132)-Net over F27 — Constructive and digital
Digital (22, 49, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 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, 32, 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, 17, 64)-net over F27, using
(22, 49, 172)-Net in Base 27 — Constructive
(22, 49, 172)-net in base 27, using
- 11 times m-reduction [i] based on (22, 60, 172)-net in base 27, using
- base change [i] based on digital (7, 45, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 45, 172)-net over F81, using
(22, 49, 209)-Net over F27 — Digital
Digital (22, 49, 209)-net over F27, using
(22, 49, 244)-Net in Base 27
(22, 49, 244)-net in base 27, using
- 3 times m-reduction [i] based on (22, 52, 244)-net in base 27, using
- base change [i] based on digital (9, 39, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 39, 244)-net over F81, using
(22, 49, 42014)-Net in Base 27 — Upper bound on s
There is no (22, 49, 42015)-net in base 27, because
- 1 times m-reduction [i] would yield (22, 48, 42015)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 507 578639 055610 518662 532847 859825 161292 847295 707450 563110 526748 258543 > 2748 [i]