MinT - Best Known (100, 120, s)-Nets in Base 4

Best Known (100, 120, s)-Nets in Base 4

Digital (100, 120, 6553)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹²⁰, 6553, F₄, 20, 20) (dual of [(6553, 20), 130940, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4¹²⁰, 65530, F₄, 20) (dual of [65530, 65410, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹²⁰, 65535, F₄, 20) (dual of [65535, 65415, 21]-code), using
    - 1 times truncation [i] based on linear OA(4¹²¹, 65536, F₄, 21) (dual of [65536, 65415, 22]-code), using
      - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Digital (100, 120, 32767)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹²⁰, 32767, F₄, 2, 20) (dual of [(32767, 2), 65414, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹²⁰, 65534, F₄, 20) (dual of [65534, 65414, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹²⁰, 65535, F₄, 20) (dual of [65535, 65415, 21]-code), using
    - 1 times truncation [i] based on linear OA(4¹²¹, 65536, F₄, 21) (dual of [65536, 65415, 22]-code), using
      - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

There is no (100, 120, large)-net in base 4, because

18 times m-reduction [i] would yield (100, 102, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]