Best Known (213−147, 213, s)-Nets in Base 2
(213−147, 213, 43)-Net over F2 — Constructive and digital
Digital (66, 213, 43)-net over F2, using
- t-expansion [i] based on digital (59, 213, 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
(213−147, 213, 48)-Net over F2 — Digital
Digital (66, 213, 48)-net over F2, using
- t-expansion [i] based on digital (65, 213, 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
(213−147, 213, 97)-Net in Base 2 — Upper bound on s
There is no (66, 213, 98)-net in base 2, because
- 25 times m-reduction [i] would yield (66, 188, 98)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2188, 98, S2, 2, 122), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 50216 813883 093446 110686 315385 661331 328818 843555 712276 103168 / 123 > 2188 [i]
- extracting embedded OOA [i] would yield OOA(2188, 98, S2, 2, 122), but