MinT - Best Known (255−22, 255, s)-Nets in Base 4

Best Known (255−22, 255, s)-Nets in Base 4

Digital (233, 255, 2287800)-net over F₄, using

trace code for nets [i] based on digital (63, 85, 762600)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁸⁵, 762600, F₆₄, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(64⁸⁵, 8388600, F₆₄, 22) (dual of [8388600, 8388515, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁸⁵, large, F₆₄, 22) (dual of [large, large−85, 23]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Digital (233, 255, large)-net over F₄, using

t-expansion [i] based on digital (231, 255, large)-net over F₄, using
- 2 times m-reduction [i] based on digital (231, 257, large)-net over F₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²⁵⁷, large, F₄, 26) (dual of [large, large−257, 27]-code), using
    - 28 times code embedding in larger space [i] based on linear OA(4²²⁹, large, F₄, 26) (dual of [large, large−229, 27]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

There is no (233, 255, large)-net in base 4, because

20 times m-reduction [i] would yield (233, 235, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]