Best Known (68, 68+53, s)-Nets in Base 2
(68, 68+53, 43)-Net over F2 — Constructive and digital
Digital (68, 121, 43)-net over F2, using
- t-expansion [i] based on digital (59, 121, 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
(68, 68+53, 50)-Net over F2 — Digital
Digital (68, 121, 50)-net over F2, using
(68, 68+53, 222)-Net in Base 2 — Upper bound on s
There is no (68, 121, 223)-net in base 2, because
- 1 times m-reduction [i] would yield (68, 120, 223)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 392879 674639 888031 151274 139741 904765 > 2120 [i]