MinT - Best Known (104, 125, s)-Nets in Base 3

Best Known (104, 125, s)-Nets in Base 3

Digital (104, 125, 983)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹²⁵, 983, F₃, 21, 21) (dual of [(983, 21), 20518, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3¹²⁵, 9831, F₃, 21) (dual of [9831, 9706, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁵, 9840, F₃, 21) (dual of [9840, 9715, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹²⁶, 9841, F₃, 22) (dual of [9841, 9715, 23]-code), using
      - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,−1970}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Digital (104, 125, 5135)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹²⁵, 5135, F₃, 21) (dual of [5135, 5010, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹²⁵, 9840, F₃, 21) (dual of [9840, 9715, 22]-code), using
  - 1 times truncation [i] based on linear OA(3¹²⁶, 9841, F₃, 22) (dual of [9841, 9715, 23]-code), using
    - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,−1970}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

There is no (104, 125, 1867445)-net in base 3, because

1 times m-reduction [i] would yield (104, 124, 1867445)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145558 380610 655950 334031 784674 099388 192420 714290 394831 352017 > 3¹²⁴ [i]