MinT - Best Known (150−19, 150, s)-Nets in Base 9

Best Known (150−19, 150, s)-Nets in Base 9

(150−19, 150, 1864134)-Net over F₉ — Constructive and digital

Digital (131, 150, 1864134)-net over F₉, using

9¹ times duplication [i] based on digital (130, 149, 1864134)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹⁴⁹, 1864134, F₉, 21, 19) (dual of [(1864134, 21), 39146665, 20]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OOA(9¹⁴⁹, 5592403, F₉, 3, 19) (dual of [(5592403, 3), 16777060, 20]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] 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]

(150−19, 150, large)-Net over F₉ — Digital

Digital (131, 150, large)-net over F₉, using

9⁵ 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]

(150−19, 150, large)-Net in Base 9 — Upper bound on s

There is no (131, 150, large)-net in base 9, because

17 times m-reduction [i] would yield (131, 133, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]