Best Known (7, 13, s)-Nets in Base 2
(7, 13, 23)-Net over F2 — Constructive and digital
Digital (7, 13, 23)-net over F2, using
(7, 13, 27)-Net over F2 — Upper bound on s (digital)
There is no digital (7, 13, 28)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(213, 28, F2, 6) (dual of [28, 15, 7]-code), but
- adding a parity check bit [i] would yield linear OA(214, 29, F2, 7) (dual of [29, 15, 8]-code), but
(7, 13, 32)-Net in Base 2 — Upper bound on s
There is no (7, 13, 33)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 8328 > 213 [i]