MinT - Best Known (12, 12+3, s)-Nets in Base 16

Best Known (12, 12+3, s)-Nets in Base 16

(12, 12+3, large)-Net over F₁₆ — Constructive and digital

Digital (12, 15, large)-net over F₁₆, using

16⁵ times duplication [i] based on digital (7, 10, large)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16¹⁰, large, F₁₆, 3, 3), using
  - appending kth column [i] based on linear OOA(16¹⁰, large, F₁₆, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16¹⁰, large, F₁₆, 3) (dual of [large, large−10, 4]-code), using
      - product of projective cap with 16²-ovoid cap in AG(3,Â 16) [i] based on linear OA(16⁷, 66048, F₁₆, 3) (dual of [66048, 66041, 4]-code or 66048-cap in PG(6,16)), using
        product of two caps with tangent hyperplane [i]

(12, 12+3, large)-Net in Base 16 — Upper bound on s

There is no (12, 15, large)-net in base 16, because

1 times m-reduction [i] would yield (12, 14, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]