Best Known (48, 231, s)-Nets in Base 2
(48, 231, 35)-Net over F2 — Constructive and digital
Digital (48, 231, 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, 231, 36)-Net over F2 — Digital
Digital (48, 231, 36)-net over F2, using
- t-expansion [i] based on digital (47, 231, 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, 231, 59)-Net in Base 2 — Upper bound on s
There is no (48, 231, 60)-net in base 2, because
- 1 times m-reduction [i] would yield (48, 230, 60)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2230, 60, S2, 4, 182), but
- the LP bound with quadratic polynomials shows that M ≥ 322656 641712 458857 062574 836561 450939 902089 344448 965571 453848 007462 617088 / 183 > 2230 [i]
- extracting embedded OOA [i] would yield OOA(2230, 60, S2, 4, 182), but