Best Known (211−119, 211, s)-Nets in Base 2
(211−119, 211, 53)-Net over F2 — Constructive and digital
Digital (92, 211, 53)-net over F2, using
- t-expansion [i] based on digital (90, 211, 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
(211−119, 211, 60)-Net over F2 — Digital
Digital (92, 211, 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
(211−119, 211, 192)-Net in Base 2 — Upper bound on s
There is no (92, 211, 193)-net in base 2, because
- 1 times m-reduction [i] would yield (92, 210, 193)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1951 422746 043181 677964 736397 599205 340039 307886 852451 819345 776960 > 2210 [i]