MinT - Best Known (208, 208+32, s)-Nets in Base 4

Best Known (208, 208+32, s)-Nets in Base 4

Digital (208, 240, 65536)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁴⁰, 65536, F₄, 32, 32) (dual of [(65536, 32), 2096912, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(4²⁴⁰, 1048576, F₄, 32) (dual of [1048576, 1048336, 33]-code), using
  - 1 times truncation [i] based on linear OA(4²⁴¹, 1048577, F₄, 33) (dual of [1048577, 1048336, 34]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

Digital (208, 240, 349525)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²⁴⁰, 349525, F₄, 3, 32) (dual of [(349525, 3), 1048335, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4²⁴⁰, 1048575, F₄, 32) (dual of [1048575, 1048335, 33]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁴⁰, 1048576, F₄, 32) (dual of [1048576, 1048336, 33]-code), using
    - 1 times truncation [i] based on linear OA(4²⁴¹, 1048577, F₄, 33) (dual of [1048577, 1048336, 34]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

There is no (208, 240, large)-net in base 4, because

30 times m-reduction [i] would yield (208, 210, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]