Best Known (1, 5, s)-Nets in Base 4
(1, 5, 10)-Net over F4 — Constructive and digital
Digital (1, 5, 10)-net over F4, using
(1, 5, 11)-Net over F4 — Upper bound on s (digital)
There is no digital (1, 5, 12)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(45, 12, F4, 4) (dual of [12, 7, 5]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(47, 12, F4, 6) (dual of [12, 5, 7]-code), but
- discarding factors / shortening the dual code would yield linear OA(47, 10, F4, 6) (dual of [10, 3, 7]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(47, 12, F4, 6) (dual of [12, 5, 7]-code), but
(1, 5, 13)-Net in Base 4 — Upper bound on s
There is no (1, 5, 14)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1030 > 45 [i]