MinT - Best Known (95, 120, s)-Nets in Base 5

Best Known (95, 120, s)-Nets in Base 5

Digital (95, 120, 1301)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹²⁰, 1301, F₅, 25, 25) (dual of [(1301, 25), 32405, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5¹²⁰, 15613, F₅, 25) (dual of [15613, 15493, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²⁰, 15624, F₅, 25) (dual of [15624, 15504, 26]-code), using
    - 1 times truncation [i] based on linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using
      - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Digital (95, 120, 9729)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹²⁰, 9729, F₅, 25) (dual of [9729, 9609, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹²⁰, 15624, F₅, 25) (dual of [15624, 15504, 26]-code), using
  - 1 times truncation [i] based on linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using
    - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

There is no (95, 120, large)-net in base 5, because

23 times m-reduction [i] would yield (95, 97, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]