MinT - Best Known (226−23, 226, s)-Nets in Base 3

Best Known (226−23, 226, s)-Nets in Base 3

Digital (203, 226, 762600)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²²⁶, 762600, F₃, 23, 23) (dual of [(762600, 23), 17539574, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3²²⁶, 8388601, F₃, 23) (dual of [8388601, 8388375, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²⁶, large, F₃, 23) (dual of [large, large−226, 24]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Digital (203, 226, 2097150)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²²⁶, 2097150, F₃, 4, 23) (dual of [(2097150, 4), 8388374, 24]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3²²⁶, 8388600, F₃, 23) (dual of [8388600, 8388374, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²⁶, large, F₃, 23) (dual of [large, large−226, 24]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

There is no (203, 226, large)-net in base 3, because

21 times m-reduction [i] would yield (203, 205, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]