Best Known (17, 17+19, s)-Nets in Base 2
(17, 17+19, 17)-Net over F2 — Constructive and digital
Digital (17, 36, 17)-net over F2, using
- t-expansion [i] based on digital (15, 36, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(17, 17+19, 42)-Net over F2 — Upper bound on s (digital)
There is no digital (17, 36, 43)-net over F2, because
- 1 times m-reduction [i] would yield digital (17, 35, 43)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(235, 43, F2, 18) (dual of [43, 8, 19]-code), but
- adding a parity check bit [i] would yield linear OA(236, 44, F2, 19) (dual of [44, 8, 20]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(235, 43, F2, 18) (dual of [43, 8, 19]-code), but
(17, 17+19, 46)-Net in Base 2 — Upper bound on s
There is no (17, 36, 47)-net in base 2, because
- 1 times m-reduction [i] would yield (17, 35, 47)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(235, 47, S2, 18), but
- the linear programming bound shows that M ≥ 136 339441 844224 / 3705 > 235 [i]
- extracting embedded orthogonal array [i] would yield OA(235, 47, S2, 18), but