MinT - Best Known (66−9, 66, s)-Nets in Base 3

Best Known (66−9, 66, s)-Nets in Base 3

Digital (57, 66, 44286)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁶⁶, 44286, F₃, 9, 9) (dual of [(44286, 9), 398508, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁶⁶, 177145, F₃, 9) (dual of [177145, 177079, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶⁶, 177146, F₃, 9) (dual of [177146, 177080, 10]-code), using
    - 1 times truncation [i] based on linear OA(3⁶⁷, 177147, F₃, 10) (dual of [177147, 177080, 11]-code), using
      - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Digital (57, 66, 88573)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁶⁶, 88573, F₃, 2, 9) (dual of [(88573, 2), 177080, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁶⁶, 177146, F₃, 9) (dual of [177146, 177080, 10]-code), using
  - 1 times truncation [i] based on linear OA(3⁶⁷, 177147, F₃, 10) (dual of [177147, 177080, 11]-code), using
    - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

There is no (57, 66, large)-net in base 3, because