Best Known (18, 18+3, s)-Nets in Base 3
(18, 18+3, 7426048)-Net over F3 — Constructive and digital
Digital (18, 21, 7426048)-net over F3, using
- net defined by OOA [i] based on linear OOA(321, 7426048, F3, 3, 3) (dual of [(7426048, 3), 22278123, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(321, 7426048, F3, 2, 3) (dual of [(7426048, 2), 14852075, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(321, 7426048, F3, 3) (dual of [7426048, 7426027, 4]-code or 7426048-cap in PG(20,3)), using
- appending kth column [i] based on linear OOA(321, 7426048, F3, 2, 3) (dual of [(7426048, 2), 14852075, 4]-NRT-code), using
(18, 18+3, large)-Net in Base 3 — Upper bound on s
There is no (18, 21, large)-net in base 3, because
- 1 times m-reduction [i] would yield (18, 20, large)-net in base 3, but