Best Known (17−9, 17, s)-Nets in Base 2
(17−9, 17, 17)-Net over F2 — Constructive and digital
(17−9, 17, 23)-Net over F2 — Upper bound on s (digital)
There is no digital (8, 17, 24)-net over F2, because
- 1 times m-reduction [i] would yield digital (8, 16, 24)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(216, 24, F2, 8) (dual of [24, 8, 9]-code), but
- adding a parity check bit [i] would yield linear OA(217, 25, F2, 9) (dual of [25, 8, 10]-code), but
- “YH1†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(217, 25, F2, 9) (dual of [25, 8, 10]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(216, 24, F2, 8) (dual of [24, 8, 9]-code), but
(17−9, 17, 27)-Net in Base 2 — Upper bound on s
There is no (8, 17, 28)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(217, 28, S2, 2, 9), but
- the linear programming bound for OOAs shows that M ≥ 5 059415 436358 517360 951296 / 37 855140 201466 780345 > 217 [i]