MinT - Best Known (16−6, 16, s)-Nets in Base 3

Best Known (16−6, 16, s)-Nets in Base 3

Digital (10, 16, 46)-net over F₃, using

Digital (10, 16, 65)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁶, 65, F₃, 6, 6) (dual of [(65, 6), 374, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁶, 65, F₃, 5, 6) (dual of [(65, 5), 309, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁶, 65, F₃, 6) (dual of [65, 49, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁶, 80, F₃, 6) (dual of [80, 64, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

There is no (10, 16, 316)-net in base 3, because