Best Known (64−55, 64, s)-Nets in Base 27
(64−55, 64, 88)-Net over F27 — Constructive and digital
Digital (9, 64, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
(64−55, 64, 99)-Net over F27 — Digital
Digital (9, 64, 99)-net over F27, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
(64−55, 64, 904)-Net in Base 27 — Upper bound on s
There is no (9, 64, 905)-net in base 27, because
- 1 times m-reduction [i] would yield (9, 63, 905)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 502080 586673 261959 232462 023950 626966 104820 282258 597510 245304 329394 960674 208400 743263 334243 > 2763 [i]