Best Known (59, 59+170, s)-Nets in Base 2
(59, 59+170, 43)-Net over F2 — Constructive and digital
Digital (59, 229, 43)-net over F2, using
- net from sequence [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]
(59, 59+170, 75)-Net in Base 2 — Upper bound on s
There is no (59, 229, 76)-net in base 2, because
- 8 times m-reduction [i] would yield (59, 221, 76)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2221, 76, S2, 3, 162), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 647 038720 011615 355072 008362 088471 136167 291466 140973 739546 486645 981184 / 163 > 2221 [i]
- extracting embedded OOA [i] would yield OOA(2221, 76, S2, 3, 162), but