MinT - Best Known (81, 93, s)-Nets in Base 5

Best Known (81, 93, s)-Nets in Base 5

Digital (81, 93, 1398100)-net over F₅, using

5² times duplication [i] based on digital (79, 91, 1398100)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁹¹, 1398100, F₅, 12, 12) (dual of [(1398100, 12), 16777109, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(5⁹¹, 8388600, F₅, 12) (dual of [8388600, 8388509, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁹¹, large, F₅, 12) (dual of [large, large−91, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Digital (81, 93, 4194302)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5⁹³, 4194302, F₅, 2, 12) (dual of [(4194302, 2), 8388511, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(5⁹¹, 4194301, F₅, 2, 12) (dual of [(4194301, 2), 8388511, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(5⁹¹, 8388602, F₅, 12) (dual of [8388602, 8388511, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁹¹, large, F₅, 12) (dual of [large, large−91, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

There is no (81, 93, large)-net in base 5, because

10 times m-reduction [i] would yield (81, 83, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]