Best Known (23, 72, s)-Nets in Base 27
(23, 72, 114)-Net over F27 — Constructive and digital
Digital (23, 72, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
(23, 72, 160)-Net in Base 27 — Constructive
(23, 72, 160)-net in base 27, using
- base change [i] based on digital (5, 54, 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
(23, 72, 163)-Net over F27 — Digital
Digital (23, 72, 163)-net over F27, using
- t-expansion [i] based on digital (21, 72, 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
(23, 72, 167)-Net in Base 27
(23, 72, 167)-net in base 27, using
- base change [i] based on digital (5, 54, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
(23, 72, 6456)-Net in Base 27 — Upper bound on s
There is no (23, 72, 6457)-net in base 27, because
- 1 times m-reduction [i] would yield (23, 71, 6457)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 424052 134213 308969 198569 126533 468866 352935 104912 885220 892607 474252 821846 387052 224011 048788 797115 761569 > 2771 [i]