Best Known (214−183, 214, s)-Nets in Base 2
(214−183, 214, 21)-Net over F2 — Constructive and digital
Digital (31, 214, 21)-net over F2, using
- t-expansion [i] based on digital (21, 214, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(214−183, 214, 27)-Net over F2 — Digital
Digital (31, 214, 27)-net over F2, using
- net from sequence [i] based on digital (31, 26)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 31 and N(F) ≥ 27, using
(214−183, 214, 39)-Net in Base 2 — Upper bound on s
There is no (31, 214, 40)-net in base 2, because
- 22 times m-reduction [i] would yield (31, 192, 40)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2192, 40, S2, 5, 161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 200867 255532 373784 442745 261542 645325 315275 374222 849104 412672 / 27 > 2192 [i]
- extracting embedded OOA [i] would yield OOA(2192, 40, S2, 5, 161), but