Best Known (69, 69+153, s)-Nets in Base 2
(69, 69+153, 48)-Net over F2 — Constructive and digital
Digital (69, 222, 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, 69+153, 49)-Net over F2 — Digital
Digital (69, 222, 49)-net over F2, using
- t-expansion [i] based on digital (68, 222, 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, 69+153, 101)-Net in Base 2 — Upper bound on s
There is no (69, 222, 102)-net in base 2, because
- 25 times m-reduction [i] would yield (69, 197, 102)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2197, 102, S2, 2, 128), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12 855504 354071 922204 335696 738729 300820 177623 950262 342682 411008 / 43 > 2197 [i]
- extracting embedded OOA [i] would yield OOA(2197, 102, S2, 2, 128), but