MinT - Best Known (21, 24, s)-Nets in Base 3

Best Known (21, 24, s)-Nets in Base 3

(21, 24, large)-Net over F₃ — Constructive and digital

Digital (21, 24, large)-net over F₃, using

3² times duplication [i] based on digital (19, 22, large)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3²², large, F₃, 3, 3), using
  - appending kth column [i] based on linear OOA(3²², large, F₃, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3²², large, F₃, 3) (dual of [large, large−22, 4]-code), using
      - doubling the cap [i] based on linear OA(3²¹, 7426048, F₃, 3) (dual of [7426048, 7426027, 4]-code or 7426048-cap in PG(20,3)), using
        doubling the cap [i] based on linear OA(3²⁰, 3713024, F₃, 3) (dual of [3713024, 3713004, 4]-code or 3713024-cap in PG(19,3)), using
        large caps in PG(u,Â 3) [i]

(21, 24, large)-Net in Base 3 — Upper bound on s

There is no (21, 24, large)-net in base 3, because

1 times m-reduction [i] would yield (21, 23, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]