Best Known (107−45, 107, s)-Nets in Base 2
(107−45, 107, 43)-Net over F2 — Constructive and digital
Digital (62, 107, 43)-net over F2, using
- t-expansion [i] based on digital (59, 107, 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
(107−45, 107, 50)-Net over F2 — Digital
Digital (62, 107, 50)-net over F2, using
(107−45, 107, 224)-Net in Base 2 — Upper bound on s
There is no (62, 107, 225)-net in base 2, because
- 1 times m-reduction [i] would yield (62, 106, 225)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 83 335713 929325 889470 037915 993456 > 2106 [i]