MinT - Best Known (83, 95, s)-Nets in Base 9

Best Known (83, 95, s)-Nets in Base 9

(83, 95, 2796201)-Net over F₉ — Constructive and digital

Digital (83, 95, 2796201)-net over F₉, using

9² times duplication [i] based on digital (81, 93, 2796201)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁹³, 2796201, F₉, 15, 12) (dual of [(2796201, 15), 41942922, 13]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁹³, 5592403, F₉, 3, 12) (dual of [(5592403, 3), 16777116, 13]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(9⁹⁰, 5592402, F₉, 3, 12) (dual of [(5592402, 3), 16777116, 13]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁵, 2796201, F₈₁, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

(83, 95, large)-Net over F₉ — Digital

Digital (83, 95, large)-net over F₉, using

2 times m-reduction [i] based on digital (83, 97, large)-net over F₉, using
- Gilbertâ€“VarÅ¡amov bound [i]

(83, 95, large)-Net in Base 9 — Upper bound on s

There is no (83, 95, large)-net in base 9, because

10 times m-reduction [i] would yield (83, 85, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]