Best Known (7−3, 7, s)-Nets in Base 16
(7−3, 7, 66048)-Net over F16 — Constructive and digital
Digital (4, 7, 66048)-net over F16, using
- net defined by OOA [i] based on linear OOA(167, 66048, F16, 3, 3) (dual of [(66048, 3), 198137, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(167, 66048, F16, 2, 3) (dual of [(66048, 2), 132089, 4]-NRT-code), using
(7−3, 7, 945411)-Net over F16 — Upper bound on s (digital)
There is no digital (4, 7, 945412)-net over F16, because
- extracting embedded orthogonal array [i] would yield linear OA(167, 945412, F16, 3) (dual of [945412, 945405, 4]-code or 945412-cap in PG(6,16)), but
- removing affine subspaces [i] would yield
- linear OA(165, 3934, F16, 3) (dual of [3934, 3929, 4]-code or 3934-cap in PG(4,16)), but
- 58269-cap in AG(5,16), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 257-cap in AG(3,16), but
- 883211-cap in AG(6,16), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 257-cap in AG(3,16) (see above)
- removing affine subspaces [i] would yield
(7−3, 7, 1118480)-Net in Base 16 — Upper bound on s
There is no (4, 7, 1118481)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(167, 1118481, S16, 3), but