Best Known (54, ∞, s)-Nets in Base 2
(54, ∞, 42)-Net over F2 — Constructive and digital
Digital (54, m, 42)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
(54, ∞, 62)-Net in Base 2 — Upper bound on s
There is no (54, m, 63)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (54, 433, 63)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2433, 63, S2, 7, 379), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 140501 003861 269071 594535 750158 460619 052929 422190 130396 031610 236234 487649 625942 980986 860241 512395 754291 186014 862203 557451 968049 840128 / 95 > 2433 [i]
- extracting embedded OOA [i] would yield OOA(2433, 63, S2, 7, 379), but