MinT - Best Known (29, 39, s)-Nets in Base 5

Best Known (29, 39, s)-Nets in Base 5

Digital (29, 39, 312)-net over F₅, using

net defined by OOA [i] based on linear OOA(5³⁹, 312, F₅, 10, 10) (dual of [(312, 10), 3081, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(5³⁹, 1560, F₅, 10) (dual of [1560, 1521, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(5³⁹, 1561, F₅, 10) (dual of [1561, 1522, 11]-code), using
    - 1 times truncation [i] based on linear OA(5⁴⁰, 1562, F₅, 11) (dual of [1562, 1522, 12]-code), using
      - the BCH-code C(I) with length 1562Â | 5⁵âˆ’1, defining interval IÂ =Â {625,802,979,…,−729}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Digital (29, 39, 1561)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5³⁹, 1561, F₅, 10) (dual of [1561, 1522, 11]-code), using
- 1 times truncation [i] based on linear OA(5⁴⁰, 1562, F₅, 11) (dual of [1562, 1522, 12]-code), using
  - the BCH-code C(I) with length 1562Â | 5⁵âˆ’1, defining interval IÂ =Â {625,802,979,…,−729}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

There is no (29, 39, 184389)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1818 997193 184861 453663 443013 > 5³⁹ [i]