MinT - Best Known (38, 38+10, s)-Nets in Base 9

Best Known (38, 38+10, s)-Nets in Base 9

(38, 38+10, 11845)-Net over F₉ — Constructive and digital

Digital (38, 48, 11845)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 7, 36)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁷, 36, F₉, 5, 5) (dual of [(36, 5), 173, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
      - a code by Danev and Olsson [i]
2. digital (31, 41, 11809)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁴¹, 11809, F₉, 10, 10) (dual of [(11809, 10), 118049, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(9⁴¹, 59045, F₉, 10) (dual of [59045, 59004, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁴¹, 59049, F₉, 10) (dual of [59049, 59008, 11]-code), using
        an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

(38, 38+10, 63677)-Net over F₉ — Digital

Digital (38, 48, 63677)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+10, large)-Net in Base 9 — Upper bound on s

There is no (38, 48, large)-net in base 9, because

8 times m-reduction [i] would yield (38, 40, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]