MinT - Best Known (10, 10+3, s)-Nets in Base 32

Best Known (10, 10+3, s)-Nets in Base 32

(10, 10+3, large)-Net over F₃₂ — Constructive and digital

Digital (10, 13, large)-net over F₃₂, using

32⁴ times duplication [i] based on digital (6, 9, large)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁹, large, F₃₂, 3, 3), using
  - appending kth column [i] based on linear OOA(32⁹, large, F₃₂, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(32⁹, large, F₃₂, 3) (dual of [large, large−9, 4]-code), using
      - product of projective cap with (hyper)oval [i] based on linear OA(32⁷, 1050624, F₃₂, 3) (dual of [1050624, 1050617, 4]-code or 1050624-cap in PG(6,32)), using
        product of two caps with tangent hyperplane [i]

(10, 10+3, large)-Net in Base 32 — Upper bound on s

There is no (10, 13, large)-net in base 32, because

1 times m-reduction [i] would yield (10, 12, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]