MinT - Best Known (36−4, 36, s)-Nets in Base 9

Best Known (36−4, 36, s)-Nets in Base 9

(36−4, 36, large)-Net over F₉ — Constructive and digital

Digital (32, 36, large)-net over F₉, using

t-expansion [i] based on digital (31, 36, large)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 2, 10)-net over F₉, using
    - kÂ =Â 2 construction [i]
  2. digital (29, 34, 8388602)-net over F₉, using
    - trace code for nets [i] based on digital (12, 17, 4194301)-net over F₈₁, using
      - net defined by OOA [i] based on linear OOA(81¹⁷, 4194301, F₈₁, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
        appending kth column [i] based on linear OOA(81¹⁷, 4194301, F₈₁, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]

(36−4, 36, large)-Net in Base 9 — Upper bound on s

There is no (32, 36, large)-net in base 9, because

2 times m-reduction [i] would yield (32, 34, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]