MinT - Best Known (120−15, 120, s)-Nets in Base 3

Best Known (120−15, 120, s)-Nets in Base 3

Digital (105, 120, 75919)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹²⁰, 75919, F₃, 15, 15) (dual of [(75919, 15), 1138665, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3¹²⁰, 531434, F₃, 15) (dual of [531434, 531314, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁰, 531440, F₃, 15) (dual of [531440, 531320, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (105, 120, 177146)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹²⁰, 177146, F₃, 3, 15) (dual of [(177146, 3), 531318, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹²⁰, 531438, F₃, 15) (dual of [531438, 531318, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁰, 531440, F₃, 15) (dual of [531440, 531320, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (105, 120, large)-net in base 3, because

13 times m-reduction [i] would yield (105, 107, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]