Best Known (231−155, 231, s)-Nets in Base 2
(231−155, 231, 50)-Net over F2 — Constructive and digital
Digital (76, 231, 50)-net over F2, using
- t-expansion [i] based on digital (75, 231, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
(231−155, 231, 110)-Net in Base 2 — Upper bound on s
There is no (76, 231, 111)-net in base 2, because
- 16 times m-reduction [i] would yield (76, 215, 111)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2215, 111, S2, 2, 139), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 421249 166674 228746 791672 110734 681729 275580 381602 196445 017243 910144 / 7 > 2215 [i]
- extracting embedded OOA [i] would yield OOA(2215, 111, S2, 2, 139), but