Best Known (19, ∞, s)-Nets in Base 5
(19, ∞, 43)-Net over F5 — Constructive and digital
Digital (19, m, 43)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 42)-sequence over F5, using
- t-expansion [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (18, 42)-sequence over F5, using
(19, ∞, 45)-Net over F5 — Digital
Digital (19, m, 45)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(19, ∞, 90)-Net in Base 5 — Upper bound on s
There is no (19, m, 91)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (19, 269, 91)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5269, 91, S5, 3, 250), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 37424 802698 468357 446437 437882 008567 477370 362907 408201 802776 058739 133912 232942 646552 488832 565095 975591 174246 696177 772590 050454 835523 990979 934653 519785 835162 902998 263234 621845 185756 683349 609375 / 251 > 5269 [i]
- extracting embedded OOA [i] would yield OOA(5269, 91, S5, 3, 250), but