Best Known (162−72, 162, s)-Nets in Base 2
(162−72, 162, 53)-Net over F2 — Constructive and digital
Digital (90, 162, 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]
(162−72, 162, 61)-Net over F2 — Digital
Digital (90, 162, 61)-net over F2, using
(162−72, 162, 273)-Net in Base 2 — Upper bound on s
There is no (90, 162, 274)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 296609 842141 929484 907938 784766 256213 387616 491680 > 2162 [i]