MinT - Best Known (61, 61+21, s)-Nets in Base 9

Best Known (61, 61+21, s)-Nets in Base 9

Digital (61, 82, 1312)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁸², 1312, F₉, 21, 21) (dual of [(1312, 21), 27470, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9⁸², 13121, F₉, 21) (dual of [13121, 13039, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁸², 13124, F₉, 21) (dual of [13124, 13042, 22]-code), using
    - trace code [i] based on linear OA(81⁴¹, 6562, F₈₁, 21) (dual of [6562, 6521, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (61, 82, 11583)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁸², 11583, F₉, 21) (dual of [11583, 11501, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁸², 13124, F₉, 21) (dual of [13124, 13042, 22]-code), using
  - trace code [i] based on linear OA(81⁴¹, 6562, F₈₁, 21) (dual of [6562, 6521, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’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 9, because

19 times m-reduction [i] would yield (61, 63, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]