MinT - Best Known (60, 60+12, s)-Nets in Base 3

Best Known (60, 60+12, s)-Nets in Base 3

Digital (60, 72, 3280)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁷², 3280, F₃, 12, 12) (dual of [(3280, 12), 39288, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3⁷², 19680, F₃, 12) (dual of [19680, 19608, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷², 19683, F₃, 12) (dual of [19683, 19611, 13]-code), using
    - 1 times truncation [i] based on linear OA(3⁷³, 19684, F₃, 13) (dual of [19684, 19611, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (60, 72, 9841)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁷², 9841, F₃, 2, 12) (dual of [(9841, 2), 19610, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷², 19682, F₃, 12) (dual of [19682, 19610, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷², 19683, F₃, 12) (dual of [19683, 19611, 13]-code), using
    - 1 times truncation [i] based on linear OA(3⁷³, 19684, F₃, 13) (dual of [19684, 19611, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (60, 72, 795508)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22528 527271 730987 331681 892208 557945 > 3⁷² [i]