MinT - Best Known (92, 92+13, s)-Nets in Base 3

Best Known (92, 92+13, s)-Nets in Base 3

Digital (92, 105, 265720)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁰⁵, 265720, F₃, 13, 13) (dual of [(265720, 13), 3454255, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3¹⁰⁵, 1594321, F₃, 13) (dual of [1594321, 1594216, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁵, 1594323, F₃, 13) (dual of [1594323, 1594218, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (92, 105, 529772)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁰⁵, 529772, F₃, 3, 13) (dual of [(529772, 3), 1589211, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰⁵, 531441, F₃, 3, 13) (dual of [(531441, 3), 1594218, 14]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁰⁵, 1594323, F₃, 13) (dual of [1594323, 1594218, 14]-code), using
    - an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (92, 105, large)-net in base 3, because

11 times m-reduction [i] would yield (92, 94, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]