MinT - Best Known (157−16, 157, s)-Nets in Base 3

Best Known (157−16, 157, s)-Nets in Base 3

Digital (141, 157, 1048575)-net over F₃, using

3⁶ times duplication [i] based on digital (135, 151, 1048575)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹⁵¹, 1048575, F₃, 16, 16) (dual of [(1048575, 16), 16777049, 17]-NRT-code), using
  - OA 8-folding and stacking [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Digital (141, 157, 2796203)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁵⁷, 2796203, F₃, 3, 16) (dual of [(2796203, 3), 8388452, 17]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁵¹, 2796201, F₃, 3, 16) (dual of [(2796201, 3), 8388452, 17]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

There is no (141, 157, large)-net in base 3, because

14 times m-reduction [i] would yield (141, 143, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]