MinT - Best Known (80−20, 80, s)-Nets in Base 5

Best Known (80−20, 80, s)-Nets in Base 5

Digital (60, 80, 312)-net over F₅, using

net defined by OOA [i] based on linear OOA(5⁸⁰, 312, F₅, 20, 20) (dual of [(312, 20), 6160, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5⁸⁰, 3120, F₅, 20) (dual of [3120, 3040, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁸⁰, 3125, F₅, 20) (dual of [3125, 3045, 21]-code), using
    - 1 times truncation [i] based on linear OA(5⁸¹, 3126, F₅, 21) (dual of [3126, 3045, 22]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

Digital (60, 80, 2195)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁸⁰, 2195, F₅, 20) (dual of [2195, 2115, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5⁸⁰, 3125, F₅, 20) (dual of [3125, 3045, 21]-code), using
  - 1 times truncation [i] based on linear OA(5⁸¹, 3126, F₅, 21) (dual of [3126, 3045, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]

There is no (60, 80, 442252)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 82 718695 326423 383210 270531 795000 689053 028514 747746 441025 > 5⁸⁰ [i]