Best Known (60, ∞, s)-Nets in Base 2
(60, ∞, 43)-Net over F2 — Constructive and digital
Digital (60, m, 43)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
(60, ∞, 69)-Net in Base 2 — Upper bound on s
There is no (60, m, 70)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (60, 411, 70)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2411, 70, S2, 6, 351), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 76682 492379 668837 478422 175731 801440 620094 943223 856621 437019 260251 831071 783412 116115 721948 411006 973042 320580 594902 709563 293696 / 11 > 2411 [i]
- extracting embedded OOA [i] would yield OOA(2411, 70, S2, 6, 351), but