Best Known (60, 60+105, s)-Nets in Base 2
(60, 60+105, 43)-Net over F2 — Constructive and digital
Digital (60, 165, 43)-net over F2, using
- t-expansion [i] based on digital (59, 165, 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
(60, 60+105, 114)-Net in Base 2 — Upper bound on s
There is no (60, 165, 115)-net in base 2, because
- 1 times m-reduction [i] would yield (60, 164, 115)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 23 557281 248958 798185 155222 367531 502296 212291 432776 > 2164 [i]