Best Known (252−172, 252, s)-Nets in Base 2
(252−172, 252, 51)-Net over F2 — Constructive and digital
Digital (80, 252, 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]
(252−172, 252, 56)-Net over F2 — Digital
Digital (80, 252, 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
(252−172, 252, 116)-Net in Base 2 — Upper bound on s
There is no (80, 252, 117)-net in base 2, because
- 26 times m-reduction [i] would yield (80, 226, 117)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2226, 117, S2, 2, 146), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6901 746346 790563 787434 755862 277025 452451 108972 170386 555162 524223 799296 / 49 > 2226 [i]
- extracting embedded OOA [i] would yield OOA(2226, 117, S2, 2, 146), but