MinT - Best Known (38, 43, s)-Nets in Base 5

Best Known (38, 43, s)-Nets in Base 5

Digital (38, 43, 8388602)-net over F₅, using

5¹ times duplication [i] based on digital (37, 42, 8388602)-net over F₅, using
- trace code for nets [i] based on digital (16, 21, 4194301)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25²¹, 4194301, F₂₅, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(25²¹, large, F₂₅, 5) (dual of [large, large−21, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]

Digital (38, 43, large)-net over F₅, using

t-expansion [i] based on digital (37, 43, large)-net over F₅, using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁴³, large, F₅, 6) (dual of [large, large−43, 7]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(5⁴¹, large, F₅, 6) (dual of [large, large−41, 7]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

There is no (38, 43, large)-net in base 5, because