Best Known (65, 65+157, s)-Nets in Base 2
(65, 65+157, 43)-Net over F2 — Constructive and digital
Digital (65, 222, 43)-net over F2, using
- t-expansion [i] based on digital (59, 222, 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
(65, 65+157, 48)-Net over F2 — Digital
Digital (65, 222, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
(65, 65+157, 95)-Net in Base 2 — Upper bound on s
There is no (65, 222, 96)-net in base 2, because
- 37 times m-reduction [i] would yield (65, 185, 96)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2185, 96, S2, 2, 120), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6277 101735 386680 763835 789423 207666 416102 355444 464034 512896 / 121 > 2185 [i]
- extracting embedded OOA [i] would yield OOA(2185, 96, S2, 2, 120), but