Best Known (21, 47, s)-Nets in Base 27
(21, 47, 128)-Net over F27 — Constructive and digital
Digital (21, 47, 128)-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 (4, 30, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 17, 64)-net over F27, using
(21, 47, 172)-Net in Base 27 — Constructive
(21, 47, 172)-net in base 27, using
- 9 times m-reduction [i] based on (21, 56, 172)-net in base 27, using
- base change [i] based on digital (7, 42, 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, 42, 172)-net over F81, using
(21, 47, 199)-Net over F27 — Digital
Digital (21, 47, 199)-net over F27, using
(21, 47, 244)-Net in Base 27
(21, 47, 244)-net in base 27, using
- 1 times m-reduction [i] based on (21, 48, 244)-net in base 27, using
- base change [i] based on digital (9, 36, 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, 36, 244)-net over F81, using
(21, 47, 32604)-Net in Base 27 — Upper bound on s
There is no (21, 47, 32605)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 18 801531 634140 131222 622860 583433 040438 861794 696357 050421 739483 352579 > 2747 [i]