MinT - Best Known (79, 79+8, s)-Nets in Base 4

Best Known (79, 79+8, s)-Nets in Base 4

Digital (79, 87, 6291450)-net over F₄, using

trace code for nets [i] based on digital (21, 29, 2097150)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64²⁹, 2097150, F₆₄, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
  - OA 4-folding and stacking [i] based on linear OA(64²⁹, 8388600, F₆₄, 8) (dual of [8388600, 8388571, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(64²⁹, large, F₆₄, 8) (dual of [large, large−29, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Digital (79, 87, large)-net over F₄, using

4⁶ times duplication [i] based on digital (73, 81, large)-net over F₄, using
- t-expansion [i] based on digital (72, 81, large)-net over F₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4⁸¹, large, F₄, 9) (dual of [large, large−81, 10]-code), using
    - 8 times code embedding in larger space [i] based on linear OA(4⁷³, large, F₄, 9) (dual of [large, large−73, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

There is no (79, 87, large)-net in base 4, because