Best Known (86, 86+67, s)-Nets in Base 2
(86, 86+67, 52)-Net over F2 — Constructive and digital
Digital (86, 153, 52)-net over F2, using
- t-expansion [i] based on digital (85, 153, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-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 3 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 (85, 51)-sequence over F2, using
(86, 86+67, 60)-Net over F2 — Digital
Digital (86, 153, 60)-net over F2, using
(86, 86+67, 274)-Net in Base 2 — Upper bound on s
There is no (86, 153, 275)-net in base 2, because
- 1 times m-reduction [i] would yield (86, 152, 275)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 5874 969732 259923 602112 816799 840556 674982 118432 > 2152 [i]