MinT - Best Known (29, 29+6, s)-Nets in Base 3

Best Known (29, 29+6, s)-Nets in Base 3

Digital (29, 35, 3280)-net over F₃, using

net defined by OOA [i] based on linear OOA(3³⁵, 3280, F₃, 6, 6) (dual of [(3280, 6), 19645, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(3³⁵, 3280, F₃, 5, 6) (dual of [(3280, 5), 16365, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(3³⁵, 9840, F₃, 6) (dual of [9840, 9805, 7]-code), using
    - 1 times truncation [i] based on linear OA(3³⁶, 9841, F₃, 7) (dual of [9841, 9805, 8]-code), using
      - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

Digital (29, 35, 9840)-net over F₃, using

net defined by OOA [i] based on linear OOA(3³⁵, 9840, F₃, 6, 6) (dual of [(9840, 6), 59005, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(3³⁵, 9840, F₃, 5, 6) (dual of [(9840, 5), 49165, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³⁵, 9840, F₃, 6) (dual of [9840, 9805, 7]-code), using
    - 1 times truncation [i] based on linear OA(3³⁶, 9841, F₃, 7) (dual of [9841, 9805, 8]-code), using
      - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

There is no (29, 35, 334785)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 50031 835909 787931 > 3³⁵ [i]