Best Known (15−7, 15, s)-Nets in Base 2
(15−7, 15, 23)-Net over F2 — Constructive and digital
Digital (8, 15, 23)-net over F2, using
(15−7, 15, 40)-Net over F2 — Upper bound on s (digital)
There is no digital (8, 15, 41)-net over F2, because
- 1 times m-reduction [i] would yield digital (8, 14, 41)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(214, 41, F2, 6) (dual of [41, 27, 7]-code), but
- adding a parity check bit [i] would yield linear OA(215, 42, F2, 7) (dual of [42, 27, 8]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(214, 41, F2, 6) (dual of [41, 27, 7]-code), but
(15−7, 15, 42)-Net in Base 2 — Upper bound on s
There is no (8, 15, 43)-net in base 2, because
- 1 times m-reduction [i] would yield (8, 14, 43)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 17158 > 214 [i]