Best Known (23, 23+31, s)-Nets in Base 27
(23, 23+31, 128)-Net over F27 — Constructive and digital
Digital (23, 54, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 19, 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, 35, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 19, 64)-net over F27, using
(23, 23+31, 172)-Net in Base 27 — Constructive
(23, 54, 172)-net in base 27, using
- 10 times m-reduction [i] based on (23, 64, 172)-net in base 27, using
- base change [i] based on digital (7, 48, 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, 48, 172)-net over F81, using
(23, 23+31, 174)-Net over F27 — Digital
Digital (23, 54, 174)-net over F27, using
(23, 23+31, 244)-Net in Base 27
(23, 54, 244)-net in base 27, using
- 2 times m-reduction [i] based on (23, 56, 244)-net in base 27, using
- base change [i] based on digital (9, 42, 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, 42, 244)-net over F81, using
(23, 23+31, 28194)-Net in Base 27 — Upper bound on s
There is no (23, 54, 28195)-net in base 27, because
- 1 times m-reduction [i] would yield (23, 53, 28195)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 7285 047441 694455 626699 995885 669220 786335 194609 849730 018336 331237 604324 272043 > 2753 [i]