MinT - Best Known (59, 59+12, s)-Nets in Base 3

Best Known (59, 59+12, s)-Nets in Base 3

Digital (59, 71, 1640)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁷¹, 1640, F₃, 12, 12) (dual of [(1640, 12), 19609, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3⁷¹, 9840, F₃, 12) (dual of [9840, 9769, 13]-code), using
  - 1 times truncation [i] based on linear OA(3⁷², 9841, F₃, 13) (dual of [9841, 9769, 14]-code), using
    - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,−3937}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Digital (59, 71, 4943)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁷¹, 4943, F₃, 12) (dual of [4943, 4872, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁷¹, 9840, F₃, 12) (dual of [9840, 9769, 13]-code), using
  - 1 times truncation [i] based on linear OA(3⁷², 9841, F₃, 13) (dual of [9841, 9769, 14]-code), using
    - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,−3937}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

There is no (59, 71, 662405)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7509 494870 786224 525052 437191 954753 > 3⁷¹ [i]