MinT - Best Known (38, 47, s)-Nets in Base 3

Best Known (38, 47, s)-Nets in Base 3

Digital (38, 47, 819)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁴⁷, 819, F₃, 9, 9) (dual of [(819, 9), 7324, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁴⁷, 3277, F₃, 9) (dual of [3277, 3230, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁴⁷, 3280, F₃, 9) (dual of [3280, 3233, 10]-code), using
    - 1 times truncation [i] based on linear OA(3⁴⁸, 3281, F₃, 10) (dual of [3281, 3233, 11]-code), using
      - the BCH-code C(I) with length 3281Â | 3¹⁶âˆ’1, defining interval IÂ =Â {−9,−7,−5,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Digital (38, 47, 2302)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁴⁷, 2302, F₃, 9) (dual of [2302, 2255, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁴⁷, 3280, F₃, 9) (dual of [3280, 3233, 10]-code), using
  - 1 times truncation [i] based on linear OA(3⁴⁸, 3281, F₃, 10) (dual of [3281, 3233, 11]-code), using
    - the BCH-code C(I) with length 3281Â | 3¹⁶âˆ’1, defining interval IÂ =Â {−9,−7,−5,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

There is no (38, 47, 339558)-net in base 3, because

1 times m-reduction [i] would yield (38, 46, 339558)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8863 036022 648297 834249 > 3⁴⁶ [i]