Best Known (225−133, 225, s)-Nets in Base 2
(225−133, 225, 53)-Net over F2 — Constructive and digital
Digital (92, 225, 53)-net over F2, using
- t-expansion [i] based on digital (90, 225, 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]
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
(225−133, 225, 60)-Net over F2 — Digital
Digital (92, 225, 60)-net over F2, using
- net from sequence [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
(225−133, 225, 182)-Net in Base 2 — Upper bound on s
There is no (92, 225, 183)-net in base 2, because
- 1 times m-reduction [i] would yield (92, 224, 183)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 30 150837 129303 433467 363582 524064 638041 565715 407591 398189 970054 445710 > 2224 [i]