MinT - Best Known (115, 115+15, s)-Nets in Base 3

Best Known (115, 115+15, s)-Nets in Base 3

Digital (115, 130, 227760)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹³⁰, 227760, F₃, 15, 15) (dual of [(227760, 15), 3416270, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3¹³⁰, 1594321, F₃, 15) (dual of [1594321, 1594191, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹³⁰, 1594322, F₃, 15) (dual of [1594322, 1594192, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹³¹, 1594323, F₃, 16) (dual of [1594323, 1594192, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (115, 130, 531440)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹³⁰, 531440, F₃, 3, 15) (dual of [(531440, 3), 1594190, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹³⁰, 1594320, F₃, 15) (dual of [1594320, 1594190, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹³⁰, 1594322, F₃, 15) (dual of [1594322, 1594192, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹³¹, 1594323, F₃, 16) (dual of [1594323, 1594192, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (115, 130, large)-net in base 3, because

13 times m-reduction [i] would yield (115, 117, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]