Best Known (72−64, 72, s)-Nets in Base 27
(72−64, 72, 84)-Net over F27 — Constructive and digital
Digital (8, 72, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
(72−64, 72, 92)-Net over F27 — Digital
Digital (8, 72, 92)-net over F27, using
- net from sequence [i] based on digital (8, 91)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 92, using
(72−64, 72, 797)-Net in Base 27 — Upper bound on s
There is no (8, 72, 798)-net in base 27, because
- 4 times m-reduction [i] would yield (8, 68, 798)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 21 759841 323755 325293 592541 572526 435948 734402 247472 602110 015719 661290 027168 675913 479592 041960 443733 > 2768 [i]