Best Known (254−172, 254, s)-Nets in Base 2
(254−172, 254, 51)-Net over F2 — Constructive and digital
Digital (82, 254, 51)-net over F2, using
- t-expansion [i] based on digital (80, 254, 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
(254−172, 254, 56)-Net over F2 — Digital
Digital (82, 254, 56)-net over F2, using
- t-expansion [i] based on digital (80, 254, 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
(254−172, 254, 118)-Net in Base 2 — Upper bound on s
There is no (82, 254, 119)-net in base 2, because
- 23 times m-reduction [i] would yield (82, 231, 119)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2231, 119, S2, 2, 149), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 55213 970774 324510 299478 046898 216203 619608 871777 363092 441300 193790 394368 / 15 > 2231 [i]
- extracting embedded OOA [i] would yield OOA(2231, 119, S2, 2, 149), but