Best Known (48, 48+77, s)-Nets in Base 2
(48, 48+77, 35)-Net over F2 — Constructive and digital
Digital (48, 125, 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]
(48, 48+77, 36)-Net over F2 — Digital
Digital (48, 125, 36)-net over F2, using
- t-expansion [i] based on digital (47, 125, 36)-net over F2, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 47 and N(F) ≥ 36, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
(48, 48+77, 96)-Net in Base 2 — Upper bound on s
There is no (48, 125, 97)-net in base 2, because
- 1 times m-reduction [i] would yield (48, 124, 97)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 26 951349 679209 496803 975468 994632 396000 > 2124 [i]