MinT - Best Known (63, 72, s)-Nets in Base 3

Best Known (63, 72, s)-Nets in Base 3

Digital (63, 72, 132859)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁷², 132859, F₃, 9, 9) (dual of [(132859, 9), 1195659, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁷², 531437, F₃, 9) (dual of [531437, 531365, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷², 531440, F₃, 9) (dual of [531440, 531368, 10]-code), using
    - 1 times truncation [i] based on linear OA(3⁷³, 531441, F₃, 10) (dual of [531441, 531368, 11]-code), using
      - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Digital (63, 72, 265720)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁷², 265720, F₃, 2, 9) (dual of [(265720, 2), 531368, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷², 531440, F₃, 9) (dual of [531440, 531368, 10]-code), using
  - 1 times truncation [i] based on linear OA(3⁷³, 531441, F₃, 10) (dual of [531441, 531368, 11]-code), using
    - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

There is no (63, 72, large)-net in base 3, because