MinT - Best Known (241−27, 241, s)-Nets in Base 4

Best Known (241−27, 241, s)-Nets in Base 4

Digital (214, 241, 645277)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁴¹, 645277, F₄, 27, 27) (dual of [(645277, 27), 17422238, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4²⁴¹, 8388602, F₄, 27) (dual of [8388602, 8388361, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁴¹, large, F₄, 27) (dual of [large, large−241, 28]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]

Digital (214, 241, 3234097)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4²⁴¹, 3234097, F₄, 2, 27) (dual of [(3234097, 2), 6467953, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²⁴¹, 4194301, F₄, 2, 27) (dual of [(4194301, 2), 8388361, 28]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁴¹, 8388602, F₄, 27) (dual of [8388602, 8388361, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁴¹, large, F₄, 27) (dual of [large, large−241, 28]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]

There is no (214, 241, large)-net in base 4, because

25 times m-reduction [i] would yield (214, 216, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]