Best Known (69, 259, s)-Nets in Base 2
(69, 259, 48)-Net over F2 — Constructive and digital
Digital (69, 259, 48)-net over F2, using
- net from sequence [i] based on digital (69, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using
(69, 259, 49)-Net over F2 — Digital
Digital (69, 259, 49)-net over F2, using
- t-expansion [i] based on digital (68, 259, 49)-net over F2, using
- net from sequence [i] based on digital (68, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 68 and N(F) ≥ 49, using
- net from sequence [i] based on digital (68, 48)-sequence over F2, using
(69, 259, 87)-Net in Base 2 — Upper bound on s
There is no (69, 259, 88)-net in base 2, because
- 4 times m-reduction [i] would yield (69, 255, 88)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2255, 88, S2, 3, 186), but
- the LP bound with quadratic polynomials shows that M ≥ 32 884953 343397 799500 294159 742467 365830 328675 645041 920187 205953 858247 328817 741824 / 561 > 2255 [i]
- extracting embedded OOA [i] would yield OOA(2255, 88, S2, 3, 186), but