Best Known (5, 5+49, s)-Nets in Base 81
(5, 5+49, 160)-Net over F81 — Constructive and digital
Digital (5, 54, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
(5, 5+49, 167)-Net over F81 — Digital
Digital (5, 54, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
(5, 5+49, 1996)-Net in Base 81 — Upper bound on s
There is no (5, 54, 1997)-net in base 81, because
- 1 times m-reduction [i] would yield (5, 53, 1997)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 141861 300406 254954 296083 655256 620566 790718 564230 333055 490308 482891 767905 856390 004719 453679 087996 845441 > 8153 [i]