MinT - Best Known (96−20, 96, s)-Nets in Base 5

Best Known (96−20, 96, s)-Nets in Base 5

Digital (76, 96, 1562)-net over F₅, using

net defined by OOA [i] based on linear OOA(5⁹⁶, 1562, F₅, 20, 20) (dual of [(1562, 20), 31144, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5⁹⁶, 15620, F₅, 20) (dual of [15620, 15524, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁹⁶, 15625, F₅, 20) (dual of [15625, 15529, 21]-code), using
    - 1 times truncation [i] based on linear OA(5⁹⁷, 15626, F₅, 21) (dual of [15626, 15529, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 15626Â | 5¹²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (76, 96, 9215)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁹⁶, 9215, F₅, 20) (dual of [9215, 9119, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5⁹⁶, 15625, F₅, 20) (dual of [15625, 15529, 21]-code), using
  - 1 times truncation [i] based on linear OA(5⁹⁷, 15626, F₅, 21) (dual of [15626, 15529, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 15626Â | 5¹²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

There is no (76, 96, 5808017)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 621788 639378 259691 453852 488915 340491 554651 801636 495033 024444 074233 > 5⁹⁶ [i]