MinT - Best Known (108, 128, s)-Nets in Base 5

Best Known (108, 128, s)-Nets in Base 5

Digital (108, 128, 39062)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹²⁸, 39062, F₅, 20, 20) (dual of [(39062, 20), 781112, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5¹²⁸, 390620, F₅, 20) (dual of [390620, 390492, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²⁸, 390625, F₅, 20) (dual of [390625, 390497, 21]-code), using
    - 1 times truncation [i] based on linear OA(5¹²⁹, 390626, F₅, 21) (dual of [390626, 390497, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 390626Â | 5¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (108, 128, 195312)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹²⁸, 195312, F₅, 2, 20) (dual of [(195312, 2), 390496, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹²⁸, 390624, F₅, 20) (dual of [390624, 390496, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²⁸, 390625, F₅, 20) (dual of [390625, 390497, 21]-code), using
    - 1 times truncation [i] based on linear OA(5¹²⁹, 390626, F₅, 21) (dual of [390626, 390497, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 390626Â | 5¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

There is no (108, 128, large)-net in base 5, because

18 times m-reduction [i] would yield (108, 110, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]