Best Known (17, 72, s)-Nets in Base 2
(17, 72, 17)-Net over F2 — Constructive and digital
Digital (17, 72, 17)-net over F2, using
- t-expansion [i] based on digital (15, 72, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(17, 72, 29)-Net in Base 2 — Upper bound on s
There is no (17, 72, 30)-net in base 2, because
- 17 times m-reduction [i] would yield (17, 55, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(255, 30, S2, 2, 38), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 576460 752303 423488 / 13 > 255 [i]
- extracting embedded OOA [i] would yield OOA(255, 30, S2, 2, 38), but