MinT - Best Known (125, 125+20, s)-Nets in Base 8

Best Known (125, 125+20, s)-Nets in Base 8

Digital (125, 145, 838860)-net over F₈, using

t-expansion [i] based on digital (124, 145, 838860)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹⁴⁵, 838860, F₈, 21, 21) (dual of [(838860, 21), 17615915, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(8¹⁴⁵, 8388601, F₈, 21) (dual of [8388601, 8388456, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹⁴⁵, large, F₈, 21) (dual of [large, large−145, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (125, 145, large)-net over F₈, using

1 times m-reduction [i] based on digital (125, 146, large)-net over F₈, using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁴⁶, large, F₈, 21) (dual of [large, large−146, 22]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(8¹⁴⁵, large, F₈, 21) (dual of [large, large−145, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

There is no (125, 145, large)-net in base 8, because

18 times m-reduction [i] would yield (125, 127, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]