Best Known (16−8, 16, s)-Nets in Base 2
(16−8, 16, 19)-Net over F2 — Constructive and digital
Digital (8, 16, 19)-net over F2, using
(16−8, 16, 23)-Net over F2 — Upper bound on s (digital)
There is no digital (8, 16, 24)-net over F2, because
- 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
(16−8, 16, 30)-Net in Base 2 — Upper bound on s
There is no (8, 16, 31)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 71301 > 216 [i]