MinT - Best Known (95−10, 95, s)-Nets in Base 3

Best Known (95−10, 95, s)-Nets in Base 3

(95−10, 95, 1677720)-Net over F₃ — Constructive and digital

Digital (85, 95, 1677720)-net over F₃, using

3⁴ times duplication [i] based on digital (81, 91, 1677720)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁹¹, 1677720, F₃, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(3⁹¹, 8388600, F₃, 10) (dual of [8388600, 8388509, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(95−10, 95, 3687947)-Net over F₃ — Digital

Digital (85, 95, 3687947)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁹⁵, 3687947, F₃, 2, 10) (dual of [(3687947, 2), 7375799, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁹⁵, 4194303, F₃, 2, 10) (dual of [(4194303, 2), 8388511, 11]-NRT-code), using
  - 2 times NRT-code embedding in larger space [i] based on linear OOA(3⁹¹, 4194301, F₃, 2, 10) (dual of [(4194301, 2), 8388511, 11]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3⁹¹, 8388602, F₃, 10) (dual of [8388602, 8388511, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(95−10, 95, large)-Net in Base 3 — Upper bound on s

There is no (85, 95, large)-net in base 3, because

8 times m-reduction [i] would yield (85, 87, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]