Best Known (12, 12+15, s)-Nets in Base 5
(12, 12+15, 33)-Net over F5 — Constructive and digital
Digital (12, 27, 33)-net over F5, using
- net from sequence [i] based on digital (12, 32)-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 1 place 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]
(12, 12+15, 328)-Net in Base 5 — Upper bound on s
There is no (12, 27, 329)-net in base 5, because
- 1 times m-reduction [i] would yield (12, 26, 329)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1 498669 727791 213005 > 526 [i]