MinT - Best Known (12, 12+3, s)-Nets in Base 9

Best Known (12, 12+3, s)-Nets in Base 9

(12, 12+3, large)-Net over F₉ — Constructive and digital

Digital (12, 15, large)-net over F₉, using

9² times duplication [i] based on digital (10, 13, large)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹³, large, F₉, 3, 3), using
  - appending kth column [i] based on linear OOA(9¹³, large, F₉, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9¹³, large, F₉, 3) (dual of [large, large−13, 4]-code), using
      - doubling the cap [i] based on linear OA(9¹², 5580100, F₉, 3) (dual of [5580100, 5580088, 4]-code or 5580100-cap in PG(11,9)), using
        product of projective cap with cap in AG(5,Â 9) [i] based on linear OA(9⁷, 6723, F₉, 3) (dual of [6723, 6716, 4]-code or 6723-cap in PG(6,9)), using
        product of two caps with tangent hyperplane [i]

(12, 12+3, large)-Net in Base 9 — Upper bound on s

There is no (12, 15, large)-net in base 9, because

1 times m-reduction [i] would yield (12, 14, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]