MinT - Best Known (128, 147, s)-Nets in Base 9

Best Known (128, 147, s)-Nets in Base 9

(128, 147, 1864133)-Net over F₉ — Constructive and digital

Digital (128, 147, 1864133)-net over F₉, using

9¹ times duplication [i] based on digital (127, 146, 1864133)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹⁴⁶, 1864133, F₉, 21, 19) (dual of [(1864133, 21), 39146647, 20]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OOA(9¹⁴⁶, 5592400, F₉, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹⁴⁶, 5592402, F₉, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
      - trace code [i] based on linear OOA(81⁷³, 2796201, F₈₁, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁷³, large, F₈₁, 19) (dual of [large, large−73, 20]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

(128, 147, large)-Net over F₉ — Digital

Digital (128, 147, large)-net over F₉, using

9² times duplication [i] based on digital (126, 145, large)-net over F₉, using
- t-expansion [i] based on digital (124, 145, large)-net over F₉, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(128, 147, large)-Net in Base 9 — Upper bound on s

There is no (128, 147, large)-net in base 9, because

17 times m-reduction [i] would yield (128, 130, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]