Best Known (71, 71+∞, s)-Nets in Base 2
(71, 71+∞, 49)-Net over F2 — Constructive and digital
Digital (71, m, 49)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (71, 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
(71, 71+∞, 80)-Net in Base 2 — Upper bound on s
There is no (71, m, 81)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (71, 478, 81)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2478, 81, S2, 6, 407), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 14 438087 045211 464070 139887 187793 394164 087266 409825 491572 723600 938267 344292 041415 993056 415726 668650 366614 199556 436505 630891 446887 516708 319541 592064 / 17 > 2478 [i]
- extracting embedded OOA [i] would yield OOA(2478, 81, S2, 6, 407), but