Best Known (212−152, 212, s)-Nets in Base 2
(212−152, 212, 43)-Net over F2 — Constructive and digital
Digital (60, 212, 43)-net over F2, using
- t-expansion [i] based on digital (59, 212, 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]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(212−152, 212, 89)-Net in Base 2 — Upper bound on s
There is no (60, 212, 90)-net in base 2, because
- 40 times m-reduction [i] would yield (60, 172, 90)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2172, 90, S2, 2, 112), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 766247 770432 944429 179173 513575 154591 809369 561091 801088 / 113 > 2172 [i]
- extracting embedded OOA [i] would yield OOA(2172, 90, S2, 2, 112), but