MinT - Best Known (110−15, 110, s)-Nets in Base 3

Best Known (110−15, 110, s)-Nets in Base 3

Digital (95, 110, 25306)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹¹⁰, 25306, F₃, 15, 15) (dual of [(25306, 15), 379480, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3¹¹⁰, 177143, F₃, 15) (dual of [177143, 177033, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹¹⁰, 177146, F₃, 15) (dual of [177146, 177036, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (95, 110, 59048)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹¹⁰, 59048, F₃, 3, 15) (dual of [(59048, 3), 177034, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹¹⁰, 177144, F₃, 15) (dual of [177144, 177034, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹¹⁰, 177146, F₃, 15) (dual of [177146, 177036, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (95, 110, large)-net in base 3, because

13 times m-reduction [i] would yield (95, 97, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]