Best Known (19−14, 19, s)-Nets in Base 2
(19−14, 19, 9)-Net over F2 — Constructive and digital
Digital (5, 19, 9)-net over F2, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(19−14, 19, 11)-Net in Base 2 — Upper bound on s
There is no (5, 19, 12)-net in base 2, because
- 2 times m-reduction [i] would yield (5, 17, 12)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(217, 12, S2, 3, 12), but
- the linear programming bound for OOAs shows that M ≥ 31 881109 569536 / 235 819097 > 217 [i]
- extracting embedded OOA [i] would yield OOA(217, 12, S2, 3, 12), but