Best Known (19−3, 19, s)-Nets in Base 3
(19−3, 19, 1490944)-Net over F3 — Constructive and digital
Digital (16, 19, 1490944)-net over F3, using
- net defined by OOA [i] based on linear OOA(319, 1490944, F3, 3, 3) (dual of [(1490944, 3), 4472813, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(319, 1490944, F3, 2, 3) (dual of [(1490944, 2), 2981869, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(319, 1490944, F3, 3) (dual of [1490944, 1490925, 4]-code or 1490944-cap in PG(18,3)), using
- appending kth column [i] based on linear OOA(319, 1490944, F3, 2, 3) (dual of [(1490944, 2), 2981869, 4]-NRT-code), using
(19−3, 19, large)-Net in Base 3 — Upper bound on s
There is no (16, 19, large)-net in base 3, because
- 1 times m-reduction [i] would yield (16, 18, large)-net in base 3, but