Best Known (4, ∞, s)-Nets in Base 4
(4, ∞, 15)-Net over F4 — Constructive and digital
Digital (4, m, 15)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
(4, ∞, 20)-Net in Base 4 — Upper bound on s
There is no (4, m, 21)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (4, 24, 21)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(424, 21, S4, 2, 20), but
- the linear programming bound for OOAs shows that M ≥ 106960 491150 049280 / 311 > 424 [i]
- extracting embedded OOA [i] would yield OOA(424, 21, S4, 2, 20), but