Best Known (248−163, 248, s)-Nets in Base 2
(248−163, 248, 52)-Net over F2 — Constructive and digital
Digital (85, 248, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 3 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(248−163, 248, 57)-Net over F2 — Digital
Digital (85, 248, 57)-net over F2, using
- t-expansion [i] based on digital (83, 248, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(248−163, 248, 122)-Net in Base 2 — Upper bound on s
There is no (85, 248, 123)-net in base 2, because
- 9 times m-reduction [i] would yield (85, 239, 123)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2239, 123, S2, 2, 154), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 269553 036454 149273 332760 011886 696253 239742 350009 903329 945699 220681 916416 / 31 > 2239 [i]
- extracting embedded OOA [i] would yield OOA(2239, 123, S2, 2, 154), but