Best Known (4, 4+3, s)-Nets in Base 7
(4, 4+3, 2499)-Net over F7 — Constructive and digital
Digital (4, 7, 2499)-net over F7, using
- net defined by OOA [i] based on linear OOA(77, 2499, F7, 3, 3) (dual of [(2499, 3), 7490, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(77, 2499, F7, 2, 3) (dual of [(2499, 2), 4991, 4]-NRT-code), using
(4, 4+3, 11392)-Net over F7 — Upper bound on s (digital)
There is no digital (4, 7, 11393)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(77, 11393, F7, 3) (dual of [11393, 11386, 4]-code or 11393-cap in PG(6,7)), but
- removing affine subspaces [i] would yield
- linear OA(76, 1659, F7, 3) (dual of [1659, 1653, 4]-code or 1659-cap in PG(5,7)), but
- 9735-cap in AG(6,7), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7), but
- removing affine subspaces [i] would yield
(4, 4+3, 19607)-Net in Base 7 — Upper bound on s
There is no (4, 7, 19608)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(77, 19608, S7, 3), but