Best Known (10, 29, s)-Nets in Base 2
(10, 29, 12)-Net over F2 — Constructive and digital
Digital (10, 29, 12)-net over F2, using
- t-expansion [i] based on digital (9, 29, 12)-net over F2, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 9 and N(F) ≥ 12, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
(10, 29, 13)-Net over F2 — Digital
Digital (10, 29, 13)-net over F2, using
- net from sequence [i] based on digital (10, 12)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 10 and N(F) ≥ 13, using
(10, 29, 20)-Net in Base 2 — Upper bound on s
There is no (10, 29, 21)-net in base 2, because
- 1 times m-reduction [i] would yield (10, 28, 21)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(228, 21, S2, 2, 18), but
- the linear programming bound for OOAs shows that M ≥ 40 743401 947136 / 150793 > 228 [i]
- extracting embedded OOA [i] would yield OOA(228, 21, S2, 2, 18), but