Best Known (59, 59+138, s)-Nets in Base 2
(59, 59+138, 43)-Net over F2 — Constructive and digital
Digital (59, 197, 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+138, 87)-Net in Base 2 — Upper bound on s
There is no (59, 197, 88)-net in base 2, because
- 28 times m-reduction [i] would yield (59, 169, 88)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2169, 88, S2, 2, 110), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 95780 971304 118053 647396 689196 894323 976171 195136 475136 / 111 > 2169 [i]
- extracting embedded OOA [i] would yield OOA(2169, 88, S2, 2, 110), but