MinT - Best Known (103, 103+14, s)-Nets in Base 5

Best Known (103, 103+14, s)-Nets in Base 5

Digital (103, 117, 1198371)-net over F₅, using

5⁶ times duplication [i] based on digital (97, 111, 1198371)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹¹¹, 1198371, F₅, 14, 14) (dual of [(1198371, 14), 16777083, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(5¹¹¹, 8388597, F₅, 14) (dual of [8388597, 8388486, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹¹¹, large, F₅, 14) (dual of [large, large−111, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Digital (103, 117, 7551114)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹¹⁷, 7551114, F₅, 14) (dual of [7551114, 7550997, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹¹⁷, large, F₅, 14) (dual of [large, large−117, 15]-code), using
  - 6 times code embedding in larger space [i] based on linear OA(5¹¹¹, large, F₅, 14) (dual of [large, large−111, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

There is no (103, 117, large)-net in base 5, because

12 times m-reduction [i] would yield (103, 105, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]