MinT - Best Known (74, 74+16, s)-Nets in Base 3

Best Known (74, 74+16, s)-Nets in Base 3

Digital (74, 90, 1230)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁹⁰, 1230, F₃, 16, 16) (dual of [(1230, 16), 19590, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3⁹⁰, 9840, F₃, 16) (dual of [9840, 9750, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹⁰, 9841, F₃, 16) (dual of [9841, 9751, 17]-code), using
    - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,−1}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Digital (74, 90, 4798)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁹⁰, 4798, F₃, 2, 16) (dual of [(4798, 2), 9506, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁹⁰, 4920, F₃, 2, 16) (dual of [(4920, 2), 9750, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁹⁰, 9840, F₃, 16) (dual of [9840, 9750, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹⁰, 9841, F₃, 16) (dual of [9841, 9751, 17]-code), using
      - the BCH-code C(I) with length 9841Â | 3⁹âˆ’1, defining interval IÂ =Â {1,1313,2625,…,−1}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

There is no (74, 90, 438801)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 728099 605653 485413 684475 855559 953390 916001 > 3⁹⁰ [i]