Best Known (57−55, 57, s)-Nets in Base 81
(57−55, 57, 116)-Net over F81 — Constructive and digital
Digital (2, 57, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
(57−55, 57, 118)-Net over F81 — Digital
Digital (2, 57, 118)-net over F81, using
- net from sequence [i] based on digital (2, 117)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 118, using
(57−55, 57, 889)-Net in Base 81 — Upper bound on s
There is no (2, 57, 890)-net in base 81, because
- 35 times m-reduction [i] would yield (2, 22, 890)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 971676 444355 391183 119044 103932 902927 272001 > 8122 [i]