MinT - Best Known (93, 93+15, s)-Nets in Base 5

Best Known (93, 93+15, s)-Nets in Base 5

Digital (93, 108, 279017)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹⁰⁸, 279017, F₅, 15, 15) (dual of [(279017, 15), 4185147, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5¹⁰⁸, 1953120, F₅, 15) (dual of [1953120, 1953012, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁰⁸, 1953124, F₅, 15) (dual of [1953124, 1953016, 16]-code), using
    - 1 times truncation [i] based on linear OA(5¹⁰⁹, 1953125, F₅, 16) (dual of [1953125, 1953016, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (93, 108, 976562)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹⁰⁸, 976562, F₅, 2, 15) (dual of [(976562, 2), 1953016, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁰⁸, 1953124, F₅, 15) (dual of [1953124, 1953016, 16]-code), using
  - 1 times truncation [i] based on linear OA(5¹⁰⁹, 1953125, F₅, 16) (dual of [1953125, 1953016, 17]-code), using
    - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (93, 108, large)-net in base 5, because

13 times m-reduction [i] would yield (93, 95, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]