Best Known (7−3, 7, s)-Nets in Base 4
(7−3, 7, 288)-Net over F4 — Constructive and digital
Digital (4, 7, 288)-net over F4, using
- net defined by OOA [i] based on linear OOA(47, 288, F4, 3, 3) (dual of [(288, 3), 857, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(47, 288, F4, 2, 3) (dual of [(288, 2), 569, 4]-NRT-code), using
(7−3, 7, 607)-Net over F4 — Upper bound on s (digital)
There is no digital (4, 7, 608)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(47, 608, F4, 3) (dual of [608, 601, 4]-code or 608-cap in PG(6,4)), but
- 1 times Hill recurrence [i] would yield linear OA(46, 154, F4, 3) (dual of [154, 148, 4]-code or 154-cap in PG(5,4)), but
- construction Y1 [i] would yield
- linear OA(45, 42, F4, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
- linear OA(4148, 154, F4, 112) (dual of [154, 6, 113]-code), but
- discarding factors / shortening the dual code would yield linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code), but
- residual code [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- residual code [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(4148, 153, F4, 112) (dual of [153, 5, 113]-code), but
- construction Y1 [i] would yield
- 1 times Hill recurrence [i] would yield linear OA(46, 154, F4, 3) (dual of [154, 148, 4]-code or 154-cap in PG(5,4)), but
(7−3, 7, 1364)-Net in Base 4 — Upper bound on s
There is no (4, 7, 1365)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(47, 1365, S4, 3), but