Best Known (48, 48+75, s)-Nets in Base 2
(48, 48+75, 35)-Net over F2 — Constructive and digital
Digital (48, 123, 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+75, 36)-Net over F2 — Digital
Digital (48, 123, 36)-net over F2, using
- t-expansion [i] based on digital (47, 123, 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+75, 97)-Net in Base 2 — Upper bound on s
There is no (48, 123, 98)-net in base 2, because
- 1 times m-reduction [i] would yield (48, 122, 98)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 6 878326 654406 850055 046757 792529 937280 > 2122 [i]