Best Known (90, 253, s)-Nets in Base 2
(90, 253, 53)-Net over F2 — Constructive and digital
Digital (90, 253, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 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]
(90, 253, 57)-Net over F2 — Digital
Digital (90, 253, 57)-net over F2, using
- t-expansion [i] based on digital (83, 253, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(90, 253, 129)-Net in Base 2 — Upper bound on s
There is no (90, 253, 130)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(2253, 130, S2, 2, 163), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 694752 535423 897172 541425 910052 127447 119619 907993 843384 236745 504047 478777 839616 / 41 > 2253 [i]