Best Known (62, 62+83, s)-Nets in Base 2
(62, 62+83, 43)-Net over F2 — Constructive and digital
Digital (62, 145, 43)-net over F2, using
- t-expansion [i] based on digital (59, 145, 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
(62, 62+83, 44)-Net over F2 — Digital
Digital (62, 145, 44)-net over F2, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
(62, 62+83, 131)-Net in Base 2 — Upper bound on s
There is no (62, 145, 132)-net in base 2, because
- 1 times m-reduction [i] would yield (62, 144, 132)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 27 987016 385176 587908 326305 183229 362635 698800 > 2144 [i]