Best Known (234−159, 234, s)-Nets in Base 2
(234−159, 234, 50)-Net over F2 — Constructive and digital
Digital (75, 234, 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]
(234−159, 234, 109)-Net in Base 2 — Upper bound on s
There is no (75, 234, 110)-net in base 2, because
- 21 times m-reduction [i] would yield (75, 213, 110)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2213, 110, S2, 2, 138), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 527495 000045 372480 750032 664408 090375 653482 289613 178670 103463 460864 / 139 > 2213 [i]
- extracting embedded OOA [i] would yield OOA(2213, 110, S2, 2, 138), but