MinT - Best Known (184, 184+32, s)-Nets in Base 4

Best Known (184, 184+32, s)-Nets in Base 4

Digital (184, 216, 16384)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²¹⁶, 16384, F₄, 32, 32) (dual of [(16384, 32), 524072, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(4²¹⁶, 262144, F₄, 32) (dual of [262144, 261928, 33]-code), using
  - 1 times truncation [i] based on linear OA(4²¹⁷, 262145, F₄, 33) (dual of [262145, 261928, 34]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

Digital (184, 216, 107819)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²¹⁶, 107819, F₄, 2, 32) (dual of [(107819, 2), 215422, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²¹⁶, 131072, F₄, 2, 32) (dual of [(131072, 2), 261928, 33]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²¹⁶, 262144, F₄, 32) (dual of [262144, 261928, 33]-code), using
    - 1 times truncation [i] based on linear OA(4²¹⁷, 262145, F₄, 33) (dual of [262145, 261928, 34]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 262145Â | 4¹⁸âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

There is no (184, 216, large)-net in base 4, because

30 times m-reduction [i] would yield (184, 186, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]