Best Known (77, 77+63, s)-Nets in Base 2
(77, 77+63, 50)-Net over F2 — Constructive and digital
Digital (77, 140, 50)-net over F2, using
- t-expansion [i] based on digital (75, 140, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-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 1 place 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 (75, 49)-sequence over F2, using
(77, 77+63, 53)-Net over F2 — Digital
Digital (77, 140, 53)-net over F2, using
(77, 77+63, 235)-Net in Base 2 — Upper bound on s
There is no (77, 140, 236)-net in base 2, because
- 1 times m-reduction [i] would yield (77, 139, 236)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 776260 760164 303741 916970 125762 805561 568248 > 2139 [i]