Best Known (249−168, 249, s)-Nets in Base 2
(249−168, 249, 51)-Net over F2 — Constructive and digital
Digital (81, 249, 51)-net over F2, using
- t-expansion [i] based on digital (80, 249, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-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 2 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]
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
(249−168, 249, 56)-Net over F2 — Digital
Digital (81, 249, 56)-net over F2, using
- t-expansion [i] based on digital (80, 249, 56)-net over F2, using
- net from sequence [i] based on digital (80, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 80 and N(F) ≥ 56, using
- net from sequence [i] based on digital (80, 55)-sequence over F2, using
(249−168, 249, 117)-Net in Base 2 — Upper bound on s
There is no (81, 249, 118)-net in base 2, because
- 20 times m-reduction [i] would yield (81, 229, 118)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2229, 118, S2, 2, 148), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 165641 912322 973530 898434 140694 648610 858826 615332 089277 323900 581371 183104 / 149 > 2229 [i]
- extracting embedded OOA [i] would yield OOA(2229, 118, S2, 2, 148), but