Best Known (72−59, 72, s)-Nets in Base 27
(72−59, 72, 96)-Net over F27 — Constructive and digital
Digital (13, 72, 96)-net over F27, using
- t-expansion [i] based on digital (11, 72, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(72−59, 72, 136)-Net over F27 — Digital
Digital (13, 72, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(72−59, 72, 1418)-Net in Base 27 — Upper bound on s
There is no (13, 72, 1419)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 71, 1419)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 424926 719753 232411 512138 563282 358624 342811 144066 676643 260590 608823 312880 703313 733184 808695 313406 202951 > 2771 [i]