MinT - Best Known (19, 19+6, s)-Nets in Base 7

Best Known (19, 19+6, s)-Nets in Base 7

(19, 19+6, 2801)-Net over F₇ — Constructive and digital

Digital (19, 25, 2801)-net over F₇, using

net defined by OOA [i] based on linear OOA(7²⁵, 2801, F₇, 6, 6) (dual of [(2801, 6), 16781, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(7²⁵, 8403, F₇, 6) (dual of [8403, 8378, 7]-code), using
  - the BCH-code C(I) with length 8403Â | 7⁵âˆ’1, defining interval IÂ =Â {1,3,5,…,11}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

(19, 19+6, 8403)-Net over F₇ — Digital

Digital (19, 25, 8403)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7²⁵, 8403, F₇, 6) (dual of [8403, 8378, 7]-code), using
- the BCH-code C(I) with length 8403Â | 7⁵âˆ’1, defining interval IÂ =Â {1,3,5,…,11}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

(19, 19+6, 3339765)-Net in Base 7 — Upper bound on s

There is no (19, 25, 3339766)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1341 069246 382387 412233 > 7²⁵ [i]