Best Known (6, 6+64, s)-Nets in Base 27
(6, 6+64, 76)-Net over F27 — Constructive and digital
Digital (6, 70, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
(6, 6+64, 612)-Net in Base 27 — Upper bound on s
There is no (6, 70, 613)-net in base 27, because
- 18 times m-reduction [i] would yield (6, 52, 613)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 271 938324 575646 848595 615128 543363 221547 752737 643934 131877 501219 467269 460707 > 2752 [i]