Best Known (197−123, 197, s)-Nets in Base 2
(197−123, 197, 49)-Net over F2 — Constructive and digital
Digital (74, 197, 49)-net over F2, using
- t-expansion [i] based on digital (70, 197, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [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 (70, 48)-sequence over F2, using
(197−123, 197, 141)-Net in Base 2 — Upper bound on s
There is no (74, 197, 142)-net in base 2, because
- 1 times m-reduction [i] would yield (74, 196, 142)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 108308 457954 302908 843525 050244 106043 466619 197035 431633 087528 > 2196 [i]