Best Known (9, 16, s)-Nets in Base 2
(9, 16, 28)-Net over F2 — Constructive and digital
Digital (9, 16, 28)-net over F2, using
(9, 16, 53)-Net over F2 — Upper bound on s (digital)
There is no digital (9, 16, 54)-net over F2, because
- 1 times m-reduction [i] would yield digital (9, 15, 54)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(215, 54, F2, 6) (dual of [54, 39, 7]-code), but
- adding a parity check bit [i] would yield linear OA(216, 55, F2, 7) (dual of [55, 39, 8]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(215, 54, F2, 6) (dual of [54, 39, 7]-code), but
(9, 16, 54)-Net in Base 2 — Upper bound on s
There is no (9, 16, 55)-net in base 2, because
- 1 times m-reduction [i] would yield (9, 15, 55)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 34046 > 215 [i]