Best Known (47−31, 47, s)-Nets in Base 81
(47−31, 47, 370)-Net over F81 — Constructive and digital
Digital (16, 47, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
(47−31, 47, 57188)-Net in Base 81 — Upper bound on s
There is no (16, 47, 57189)-net in base 81, because
- 1 times m-reduction [i] would yield (16, 46, 57189)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 6171 011992 042484 074531 624930 198586 680325 429907 990110 596298 527972 099991 876564 973795 186801 > 8146 [i]