Best Known (74, 74+∞, s)-Nets in Base 2
(74, 74+∞, 49)-Net over F2 — Constructive and digital
Digital (74, m, 49)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 48)-sequence over F2, using
- t-expansion [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (70, 48)-sequence over F2, using
(74, 74+∞, 83)-Net in Base 2 — Upper bound on s
There is no (74, m, 84)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (74, 496, 84)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2496, 84, S2, 6, 422), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 820171 823688 425610 039569 090482 797456 649926 138129 194368 449874 104288 401389 214023 664649 810276 977712 471452 660052 382680 213027 651769 637656 179159 985582 768128 / 47 > 2496 [i]
- extracting embedded OOA [i] would yield OOA(2496, 84, S2, 6, 422), but