MinT - Best Known (200, 240, s)-Nets in Base 4

Best Known (200, 240, s)-Nets in Base 4

Digital (200, 240, 3276)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁴⁰, 3276, F₄, 40, 40) (dual of [(3276, 40), 130800, 41]-NRT-code), using
- OA 20-folding and stacking [i] based on linear OA(4²⁴⁰, 65520, F₄, 40) (dual of [65520, 65280, 41]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁴⁰, 65536, F₄, 40) (dual of [65536, 65296, 41]-code), using
    - 1 times truncation [i] based on linear OA(4²⁴¹, 65537, F₄, 41) (dual of [65537, 65296, 42]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]

Digital (200, 240, 32768)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²⁴⁰, 32768, F₄, 2, 40) (dual of [(32768, 2), 65296, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²⁴⁰, 65536, F₄, 40) (dual of [65536, 65296, 41]-code), using
  - 1 times truncation [i] based on linear OA(4²⁴¹, 65537, F₄, 41) (dual of [65537, 65296, 42]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]

There is no (200, 240, large)-net in base 4, because

38 times m-reduction [i] would yield (200, 202, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]