MinT - Best Known (61, 61+21, s)-Nets in Base 8

Best Known (61, 61+21, s)-Nets in Base 8

Digital (61, 82, 819)-net over F₈, using

net defined by OOA [i] based on linear OOA(8⁸², 819, F₈, 21, 21) (dual of [(819, 21), 17117, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8⁸², 8191, F₈, 21) (dual of [8191, 8109, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁸², 8194, F₈, 21) (dual of [8194, 8112, 22]-code), using
    - trace code [i] based on linear OA(64⁴¹, 4097, F₆₄, 21) (dual of [4097, 4056, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (61, 82, 8008)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8⁸², 8008, F₈, 21) (dual of [8008, 7926, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁸², 8194, F₈, 21) (dual of [8194, 8112, 22]-code), using
  - trace code [i] based on linear OA(64⁴¹, 4097, F₆₄, 21) (dual of [4097, 4056, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

There is no (61, 82, large)-net in base 8, because

19 times m-reduction [i] would yield (61, 63, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]