Best Known (248−196, 248, s)-Nets in Base 2
(248−196, 248, 36)-Net over F2 — Constructive and digital
Digital (52, 248, 36)-net over F2, using
- t-expansion [i] based on digital (51, 248, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-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 3 places 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]
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
(248−196, 248, 40)-Net over F2 — Digital
Digital (52, 248, 40)-net over F2, using
- t-expansion [i] based on digital (50, 248, 40)-net over F2, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 50 and N(F) ≥ 40, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
(248−196, 248, 63)-Net in Base 2 — Upper bound on s
There is no (52, 248, 64)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(2248, 64, S2, 4, 196), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 115792 089237 316195 423570 985008 687907 853269 984665 640564 039457 584007 913129 639936 / 197 > 2248 [i]