MinT - Best Known (241−31, 241, s)-Nets in Base 3

Best Known (241−31, 241, s)-Nets in Base 3

Digital (210, 241, 35429)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²⁴¹, 35429, F₃, 31, 31) (dual of [(35429, 31), 1098058, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3²⁴¹, 531436, F₃, 31) (dual of [531436, 531195, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴¹, 531441, F₃, 31) (dual of [531441, 531200, 32]-code), using
    - an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]

Digital (210, 241, 117846)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²⁴¹, 117846, F₃, 4, 31) (dual of [(117846, 4), 471143, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁴¹, 132860, F₃, 4, 31) (dual of [(132860, 4), 531199, 32]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3²⁴¹, 531440, F₃, 31) (dual of [531440, 531199, 32]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁴¹, 531441, F₃, 31) (dual of [531441, 531200, 32]-code), using
      - an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]

There is no (210, 241, large)-net in base 3, because

29 times m-reduction [i] would yield (210, 212, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]