Best Known (245−179, 245, s)-Nets in Base 2
(245−179, 245, 43)-Net over F2 — Constructive and digital
Digital (66, 245, 43)-net over F2, using
- t-expansion [i] based on digital (59, 245, 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
(245−179, 245, 48)-Net over F2 — Digital
Digital (66, 245, 48)-net over F2, using
- t-expansion [i] based on digital (65, 245, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
(245−179, 245, 83)-Net in Base 2 — Upper bound on s
There is no (66, 245, 84)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(2245, 84, S2, 3, 179), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 904 625697 166532 776746 648320 380374 280103 671755 200316 906558 262375 061821 325312 / 15 > 2245 [i]