Best Known (40−27, 40, s)-Nets in Base 5
(40−27, 40, 34)-Net over F5 — Constructive and digital
Digital (13, 40, 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]
(40−27, 40, 36)-Net over F5 — Digital
Digital (13, 40, 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
(40−27, 40, 168)-Net in Base 5 — Upper bound on s
There is no (13, 40, 169)-net in base 5, because
- 1 times m-reduction [i] would yield (13, 39, 169)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1951 770549 676027 162940 010037 > 539 [i]