MinT - Best Known (9−3, 9, s)-Nets in Base 256

Best Known (9−3, 9, s)-Nets in Base 256

(9−3, 9, large)-Net over F₂₅₆ — Constructive and digital

Digital (6, 9, large)-net over F₂₅₆, using

256³ times duplication [i] based on digital (3, 6, large)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁶, large, F₂₅₆, 3, 3), using
  - appending kth column [i] based on linear OOA(256⁶, large, F₂₅₆, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁶, large, F₂₅₆, 3) (dual of [large, large−6, 4]-code), using
      - product of projective cap with (hyper)oval [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]

(9−3, 9, large)-Net in Base 256 — Upper bound on s

There is no (6, 9, large)-net in base 256, because

1 times m-reduction [i] would yield (6, 8, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]