MinT - Best Known (70, 70+24, s)-Nets in Base 9

Best Known (70, 70+24, s)-Nets in Base 9

Digital (70, 94, 1093)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁹⁴, 1093, F₉, 24, 24) (dual of [(1093, 24), 26138, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9⁹⁴, 13116, F₉, 24) (dual of [13116, 13022, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁹⁴, 13122, F₉, 24) (dual of [13122, 13028, 25]-code), using
    - trace code [i] based on linear OA(81⁴⁷, 6561, F₈₁, 24) (dual of [6561, 6514, 25]-code), using
      - an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Digital (70, 94, 12222)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁹⁴, 12222, F₉, 24) (dual of [12222, 12128, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁹⁴, 13122, F₉, 24) (dual of [13122, 13028, 25]-code), using
  - trace code [i] based on linear OA(81⁴⁷, 6561, F₈₁, 24) (dual of [6561, 6514, 25]-code), using
    - an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

There is no (70, 94, large)-net in base 9, because

22 times m-reduction [i] would yield (70, 72, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]