MinT - Best Known (97, 97+12, s)-Nets in Base 4

Best Known (97, 97+12, s)-Nets in Base 4

Digital (97, 109, 1398100)-net over F₄, using

t-expansion [i] based on digital (96, 109, 1398100)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁰⁹, 1398100, F₄, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(4¹⁰⁹, 8388601, F₄, 13) (dual of [8388601, 8388492, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Digital (97, 109, 4798465)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁰⁹, 4798465, F₄, 12) (dual of [4798465, 4798356, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, large, F₄, 12) (dual of [large, large−109, 13]-code), using
  - strength reduction [i] based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

There is no (97, 109, large)-net in base 4, because

10 times m-reduction [i] would yield (97, 99, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]