MinT - Best Known (92−9, 92, s)-Nets in Base 3

Best Known (92−9, 92, s)-Nets in Base 3

Digital (83, 92, 2097150)-net over F₃, using

3² times duplication [i] based on digital (81, 90, 2097150)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁹⁰, 2097150, F₃, 9, 9) (dual of [(2097150, 9), 18874260, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(3⁹⁰, 8388601, F₃, 9) (dual of [8388601, 8388511, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹⁰, large, F₃, 9) (dual of [large, large−90, 10]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Digital (83, 92, 4194302)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁹², 4194302, F₃, 2, 9) (dual of [(4194302, 2), 8388512, 10]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3⁹⁰, 4194301, F₃, 2, 9) (dual of [(4194301, 2), 8388512, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁹⁰, 8388602, F₃, 9) (dual of [8388602, 8388512, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹⁰, large, F₃, 9) (dual of [large, large−90, 10]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

There is no (83, 92, large)-net in base 3, because