MinT - Best Known (12, 15, s)-Nets in Base 25

Best Known (12, 15, s)-Nets in Base 25

(12, 15, large)-Net over F₂₅ — Constructive and digital

Digital (12, 15, large)-net over F₂₅, using

25⁶ times duplication [i] based on digital (6, 9, large)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁹, large, F₂₅, 3, 3), using
  - appending kth column [i] based on linear OOA(25⁹, large, F₂₅, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(25⁹, large, F₂₅, 3) (dual of [large, large−9, 4]-code), using
      - product of projective cap with (hyper)oval [i] based on linear OA(25⁷, 391875, F₂₅, 3) (dual of [391875, 391868, 4]-code or 391875-cap in PG(6,25)), using
        product of two caps with tangent hyperplane [i]

(12, 15, large)-Net in Base 25 — Upper bound on s

There is no (12, 15, large)-net in base 25, because

1 times m-reduction [i] would yield (12, 14, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]