Best Known (172−139, 172, s)-Nets in Base 2
(172−139, 172, 24)-Net over F2 — Constructive and digital
Digital (33, 172, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(172−139, 172, 28)-Net over F2 — Digital
Digital (33, 172, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(172−139, 172, 42)-Net in Base 2 — Upper bound on s
There is no (33, 172, 43)-net in base 2, because
- 7 times m-reduction [i] would yield (33, 165, 43)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2165, 43, S2, 4, 132), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1122 433257 470133 441180 429951 526105 359095 756193 005568 / 19 > 2165 [i]
- extracting embedded OOA [i] would yield OOA(2165, 43, S2, 4, 132), but