MinT - Best Known (46, 46+16, s)-Nets in Base 9

Best Known (46, 46+16, s)-Nets in Base 9

Digital (46, 62, 1640)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁶², 1640, F₉, 16, 16) (dual of [(1640, 16), 26178, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(9⁶², 13120, F₉, 16) (dual of [13120, 13058, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁶², 13122, F₉, 16) (dual of [13122, 13060, 17]-code), using
    - trace code [i] based on linear OA(81³¹, 6561, F₈₁, 16) (dual of [6561, 6530, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (46, 62, 10860)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁶², 10860, F₉, 16) (dual of [10860, 10798, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁶², 13122, F₉, 16) (dual of [13122, 13060, 17]-code), using
  - trace code [i] based on linear OA(81³¹, 6561, F₈₁, 16) (dual of [6561, 6530, 17]-code), using
    - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (46, 62, large)-net in base 9, because

14 times m-reduction [i] would yield (46, 48, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]