Best Known (172−125, 172, s)-Nets in Base 2
(172−125, 172, 34)-Net over F2 — Constructive and digital
Digital (47, 172, 34)-net over F2, using
- t-expansion [i] based on digital (45, 172, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-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 1 place 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]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(172−125, 172, 36)-Net over F2 — Digital
Digital (47, 172, 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
(172−125, 172, 71)-Net in Base 2 — Upper bound on s
There is no (47, 172, 72)-net in base 2, because
- 35 times m-reduction [i] would yield (47, 137, 72)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2137, 72, S2, 2, 90), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22 300745 198530 623141 535718 272648 361505 980416 / 91 > 2137 [i]
- extracting embedded OOA [i] would yield OOA(2137, 72, S2, 2, 90), but