MinT - Best Known (14−3, 14, s)-Nets in Base 5

Best Known (14−3, 14, s)-Nets in Base 5

(14−3, 14, 1123200)-Net over F₅ — Constructive and digital

Digital (11, 14, 1123200)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹⁴, 1123200, F₅, 3, 3) (dual of [(1123200, 3), 3369586, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹⁴, 1123200, F₅, 2, 3) (dual of [(1123200, 2), 2246386, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁴, 1123200, F₅, 3) (dual of [1123200, 1123186, 4]-code or 1123200-cap in PG(13,5)), using
    - product of two projective caps and an affine cap avoiding two hyperplanes [i] based on
      1. linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
      2. linear OA(5⁷, 675, F₅, 3) (dual of [675, 668, 4]-code or 675-cap in PG(6,5)), using
        product of two caps with tangent hyperplane [i]

(14−3, 14, large)-Net in Base 5 — Upper bound on s

There is no (11, 14, large)-net in base 5, because

1 times m-reduction [i] would yield (11, 13, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]