Best Known (53−45, 53, s)-Nets in Base 27
(53−45, 53, 84)-Net over F27 — Constructive and digital
Digital (8, 53, 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
(53−45, 53, 92)-Net over F27 — Digital
Digital (8, 53, 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
(53−45, 53, 830)-Net in Base 27 — Upper bound on s
There is no (8, 53, 831)-net in base 27, because
- 1 times m-reduction [i] would yield (8, 52, 831)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 274 818515 848325 425593 824711 932704 337391 469004 557666 370219 062523 957394 569797 > 2752 [i]