MinT - Best Known (100, 100+13, s)-Nets in Base 3

Best Known (100, 100+13, s)-Nets in Base 3

Digital (100, 113, 797161)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹¹³, 797161, F₃, 13, 13) (dual of [(797161, 13), 10362980, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3¹¹³, 4782967, F₃, 13) (dual of [4782967, 4782854, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (100, 113, 1406698)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹¹³, 1406698, F₃, 3, 13) (dual of [(1406698, 3), 4219981, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹¹³, 1594323, F₃, 3, 13) (dual of [(1594323, 3), 4782856, 14]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (100, 113, large)-net in base 3, because

11 times m-reduction [i] would yield (100, 102, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]