MinT - Best Known (143−24, 143, s)-Nets in Base 3

Best Known (143−24, 143, s)-Nets in Base 3

Digital (119, 143, 820)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁴³, 820, F₃, 24, 24) (dual of [(820, 24), 19537, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3¹⁴³, 9840, F₃, 24) (dual of [9840, 9697, 25]-code), using
  - 1 times truncation [i] based on linear OA(3¹⁴⁴, 9841, F₃, 25) (dual of [9841, 9697, 26]-code), using
    - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,1966}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Digital (119, 143, 5417)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁴³, 5417, F₃, 24) (dual of [5417, 5274, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁴³, 9840, F₃, 24) (dual of [9840, 9697, 25]-code), using
  - 1 times truncation [i] based on linear OA(3¹⁴⁴, 9841, F₃, 25) (dual of [9841, 9697, 26]-code), using
    - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,1966}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

There is no (119, 143, 1282397)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 176345 345720 570416 323268 464496 333492 729072 351597 877710 896165 913841 > 3¹⁴³ [i]