MinT - Best Known (90, 90+13, s)-Nets in Base 9

Best Known (90, 90+13, s)-Nets in Base 9

(90, 90+13, 2796201)-Net over F₉ — Constructive and digital

Digital (90, 103, 2796201)-net over F₉, using

9² times duplication [i] based on digital (88, 101, 2796201)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹⁰¹, 2796201, F₉, 15, 13) (dual of [(2796201, 15), 41942914, 14]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(9¹⁰¹, 5592403, F₉, 3, 13) (dual of [(5592403, 3), 16777108, 14]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(9⁹⁸, 5592402, F₉, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁹, 2796201, F₈₁, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

(90, 90+13, large)-Net over F₉ — Digital

Digital (90, 103, large)-net over F₉, using

t-expansion [i] based on digital (89, 103, large)-net over F₉, using
- 1 times m-reduction [i] based on digital (89, 104, large)-net over F₉, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+13, large)-Net in Base 9 — Upper bound on s

There is no (90, 103, large)-net in base 9, because

11 times m-reduction [i] would yield (90, 92, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]