Best Known (44−31, 44, s)-Nets in Base 5
(44−31, 44, 34)-Net over F5 — Constructive and digital
Digital (13, 44, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 2 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(44−31, 44, 36)-Net over F5 — Digital
Digital (13, 44, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(44−31, 44, 151)-Net in Base 5 — Upper bound on s
There is no (13, 44, 152)-net in base 5, because
- 1 times m-reduction [i] would yield (13, 43, 152)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1 194350 781167 351487 565354 861665 > 543 [i]