Best Known (167−122, 167, s)-Nets in Base 2
(167−122, 167, 34)-Net over F2 — Constructive and digital
Digital (45, 167, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(167−122, 167, 68)-Net in Base 2 — Upper bound on s
There is no (45, 167, 69)-net in base 2, because
- 36 times m-reduction [i] would yield (45, 131, 69)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2131, 69, S2, 2, 86), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 87112 285931 760246 646623 899502 532662 132736 / 29 > 2131 [i]
- extracting embedded OOA [i] would yield OOA(2131, 69, S2, 2, 86), but