Best Known (62, 62+193, s)-Nets in Base 2
(62, 62+193, 43)-Net over F2 — Constructive and digital
Digital (62, 255, 43)-net over F2, using
- t-expansion [i] based on digital (59, 255, 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
(62, 62+193, 44)-Net over F2 — Digital
Digital (62, 255, 44)-net over F2, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
(62, 62+193, 79)-Net in Base 2 — Upper bound on s
There is no (62, 255, 80)-net in base 2, because
- 24 times m-reduction [i] would yield (62, 231, 80)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2231, 80, S2, 3, 169), but
- the LP bound with quadratic polynomials shows that M ≥ 980047 981244 260057 815735 332443 337614 248057 474048 194890 833078 439779 500032 / 255 > 2231 [i]
- extracting embedded OOA [i] would yield OOA(2231, 80, S2, 3, 169), but