Best Known (2, 2+6, s)-Nets in Base 2
(2, 2+6, 6)-Net over F2 — Constructive and digital
Digital (2, 8, 6)-net over F2, using
- net from sequence [i] based on digital (2, 5)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 2 and N(F) ≥ 6, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(2, 2+6, 6)-Net over F2 — Upper bound on s (digital)
There is no digital (2, 8, 7)-net over F2, because
- extracting embedded OOA [i] would yield linear OOA(28, 7, F2, 3, 6) (dual of [(7, 3), 13, 7]-NRT-code), but
(2, 2+6, 7)-Net in Base 2 — Upper bound on s
There is no (2, 8, 8)-net in base 2, because
- 1 times m-reduction [i] would yield (2, 7, 8)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(27, 8, S2, 2, 5), but
- the linear programming bound for OOAs shows that M ≥ 14080 / 103 > 27 [i]
- extracting embedded OOA [i] would yield OOA(27, 8, S2, 2, 5), but