Best Known (17, ∞, s)-Nets in Base 5
(17, ∞, 42)-Net over F5 — Constructive and digital
Digital (17, m, 42)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(17, ∞, 82)-Net in Base 5 — Upper bound on s
There is no (17, m, 83)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (17, 245, 83)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5245, 83, S5, 3, 228), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 645570 871830 419924 636880 574448 055468 740063 259242 340906 093291 881802 042574 469997 747437 486128 899560 489511 854031 317062 579653 202577 636473 581679 243949 338342 645205 557346 343994 140625 / 229 > 5245 [i]
- extracting embedded OOA [i] would yield OOA(5245, 83, S5, 3, 228), but