Best Known (12, 12+19, s)-Nets in Base 4
(12, 12+19, 28)-Net over F4 — Constructive and digital
Digital (12, 31, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
(12, 12+19, 29)-Net over F4 — Digital
Digital (12, 31, 29)-net over F4, using
- net from sequence [i] based on digital (12, 28)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 29, using
(12, 12+19, 133)-Net in Base 4 — Upper bound on s
There is no (12, 31, 134)-net in base 4, because
- 1 times m-reduction [i] would yield (12, 30, 134)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 184615 885693 965168 > 430 [i]