Best Known (168−77, 168, s)-Nets in Base 2
(168−77, 168, 53)-Net over F2 — Constructive and digital
Digital (91, 168, 53)-net over F2, using
- t-expansion [i] based on digital (90, 168, 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
(168−77, 168, 58)-Net over F2 — Digital
Digital (91, 168, 58)-net over F2, using
(168−77, 168, 263)-Net in Base 2 — Upper bound on s
There is no (91, 168, 264)-net in base 2, because
- 1 times m-reduction [i] would yield (91, 167, 264)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 192 741123 579933 539757 474412 526718 875919 898197 991688 > 2167 [i]