MinT - Best Known (99−9, 99, s)-Nets in Base 4

Best Known (99−9, 99, s)-Nets in Base 4

Digital (90, 99, 6291450)-net over F₄, using

trace code for nets [i] based on digital (24, 33, 2097150)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64³³, 2097150, F₆₄, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(64³³, 8388601, F₆₄, 9) (dual of [8388601, 8388568, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Digital (90, 99, large)-net over F₄, using

4⁷ times duplication [i] based on digital (83, 92, large)-net over F₄, using
- t-expansion [i] based on digital (82, 92, large)-net over F₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4⁹², large, F₄, 10) (dual of [large, large−92, 11]-code), using
    - 7 times code embedding in larger space [i] based on linear OA(4⁸⁵, large, F₄, 10) (dual of [large, large−85, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

There is no (90, 99, large)-net in base 4, because