Best Known (6, 6+22, s)-Nets in Base 2
(6, 6+22, 10)-Net over F2 — Constructive and digital
Digital (6, 28, 10)-net over F2, using
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 6 and N(F) ≥ 10, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(6, 6+22, 12)-Net in Base 2 — Upper bound on s
There is no (6, 28, 13)-net in base 2, because
- 7 times m-reduction [i] would yield (6, 21, 13)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(221, 13, S2, 3, 15), but
- the linear programming bound for OOAs shows that M ≥ 10 713207 389057 045770 534912 / 5 095422 688314 993735 > 221 [i]
- extracting embedded OOA [i] would yield OOA(221, 13, S2, 3, 15), but