MinT - Best Known (169−19, 169, s)-Nets in Base 4

Best Known (169−19, 169, s)-Nets in Base 4

Digital (150, 169, 932066)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁶⁹, 932066, F₄, 19, 19) (dual of [(932066, 19), 17709085, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4¹⁶⁹, 8388595, F₄, 19) (dual of [8388595, 8388426, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁹, large, F₄, 19) (dual of [large, large−169, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Digital (150, 169, 4194301)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁶⁹, 4194301, F₄, 2, 19) (dual of [(4194301, 2), 8388433, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁶⁹, 8388602, F₄, 19) (dual of [8388602, 8388433, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁹, large, F₄, 19) (dual of [large, large−169, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

There is no (150, 169, large)-net in base 4, because

17 times m-reduction [i] would yield (150, 152, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]