MinT - Best Known (81, 81+15, s)-Nets in Base 5

Best Known (81, 81+15, s)-Nets in Base 5

Digital (81, 96, 55803)-net over F₅, using

net defined by OOA [i] based on linear OOA(5⁹⁶, 55803, F₅, 15, 15) (dual of [(55803, 15), 836949, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5⁹⁶, 390622, F₅, 15) (dual of [390622, 390526, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁹⁶, 390624, F₅, 15) (dual of [390624, 390528, 16]-code), using
    - 1 times truncation [i] based on linear OA(5⁹⁷, 390625, F₅, 16) (dual of [390625, 390528, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (81, 96, 195312)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5⁹⁶, 195312, F₅, 2, 15) (dual of [(195312, 2), 390528, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5⁹⁶, 390624, F₅, 15) (dual of [390624, 390528, 16]-code), using
  - 1 times truncation [i] based on linear OA(5⁹⁷, 390625, F₅, 16) (dual of [390625, 390528, 17]-code), using
    - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (81, 96, large)-net in base 5, because

13 times m-reduction [i] would yield (81, 83, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]