MinT - Best Known (124, 124+20, s)-Nets in Base 5

Best Known (124, 124+20, s)-Nets in Base 5

Digital (124, 144, 195312)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹⁴⁴, 195312, F₅, 20, 20) (dual of [(195312, 20), 3906096, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5¹⁴⁴, 1953120, F₅, 20) (dual of [1953120, 1952976, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁴⁴, 1953125, F₅, 20) (dual of [1953125, 1952981, 21]-code), using
    - 1 times truncation [i] based on linear OA(5¹⁴⁵, 1953126, F₅, 21) (dual of [1953126, 1952981, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 1953126Â | 5¹⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (124, 144, 976562)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹⁴⁴, 976562, F₅, 2, 20) (dual of [(976562, 2), 1952980, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁴⁴, 1953124, F₅, 20) (dual of [1953124, 1952980, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁴⁴, 1953125, F₅, 20) (dual of [1953125, 1952981, 21]-code), using
    - 1 times truncation [i] based on linear OA(5¹⁴⁵, 1953126, F₅, 21) (dual of [1953126, 1952981, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 1953126Â | 5¹⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

There is no (124, 144, large)-net in base 5, because

18 times m-reduction [i] would yield (124, 126, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]