Best Known (139−89, 139, s)-Nets in Base 2
(139−89, 139, 35)-Net over F2 — Constructive and digital
Digital (50, 139, 35)-net over F2, using
- t-expansion [i] based on digital (48, 139, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
(139−89, 139, 40)-Net over F2 — Digital
Digital (50, 139, 40)-net over F2, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 50 and N(F) ≥ 40, using
(139−89, 139, 96)-Net in Base 2 — Upper bound on s
There is no (50, 139, 97)-net in base 2, because
- 1 times m-reduction [i] would yield (50, 138, 97)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 372307 197402 303057 740697 651571 030204 032240 > 2138 [i]