Best Known (76, 76+∞, s)-Nets in Base 2
(76, 76+∞, 50)-Net over F2 — Constructive and digital
Digital (76, m, 50)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (76, 49)-sequence over F2, using
- t-expansion [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [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 (75, 49)-sequence over F2, using
(76, 76+∞, 85)-Net in Base 2 — Upper bound on s
There is no (76, m, 86)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (76, 593, 86)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2593, 86, S2, 7, 517), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11 022150 729840 137546 048583 387929 646807 376810 304393 973015 613464 781990 796530 315537 263874 221848 765744 453578 025636 311267 721265 737120 044062 528161 574511 278115 216043 756264 165285 259672 289280 / 259 > 2593 [i]
- extracting embedded OOA [i] would yield OOA(2593, 86, S2, 7, 517), but