Best Known (142−106, 142, s)-Nets in Base 2
(142−106, 142, 24)-Net over F2 — Constructive and digital
Digital (36, 142, 24)-net over F2, using
- t-expansion [i] based on digital (33, 142, 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
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(142−106, 142, 30)-Net over F2 — Digital
Digital (36, 142, 30)-net over F2, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
(142−106, 142, 48)-Net in Base 2 — Upper bound on s
There is no (36, 142, 49)-net in base 2, because
- 2 times m-reduction [i] would yield (36, 140, 49)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2140, 49, S2, 3, 104), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22 300745 198530 623141 535718 272648 361505 980416 / 15 > 2140 [i]
- extracting embedded OOA [i] would yield OOA(2140, 49, S2, 3, 104), but