MinT - Best Known (108, 108+15, s)-Nets in Base 5

Best Known (108, 108+15, s)-Nets in Base 5

Digital (108, 123, 1198371)-net over F₅, using

5³ times duplication [i] based on digital (105, 120, 1198371)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹²⁰, 1198371, F₅, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(5¹²⁰, 8388598, F₅, 15) (dual of [8388598, 8388478, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹²⁰, large, F₅, 15) (dual of [large, large−120, 16]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (108, 123, 5139373)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹²³, 5139373, F₅, 15) (dual of [5139373, 5139250, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹²³, large, F₅, 15) (dual of [large, large−123, 16]-code), using
  - 3 times code embedding in larger space [i] based on linear OA(5¹²⁰, large, F₅, 15) (dual of [large, large−120, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (108, 123, large)-net in base 5, because

13 times m-reduction [i] would yield (108, 110, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]