MinT - Best Known (141−22, 141, s)-Nets in Base 3

Best Known (141−22, 141, s)-Nets in Base 3

Digital (119, 141, 5368)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁴¹, 5368, F₃, 22, 22) (dual of [(5368, 22), 117955, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3¹⁴¹, 59048, F₃, 22) (dual of [59048, 58907, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using
    - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (119, 141, 17163)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁴¹, 17163, F₃, 3, 22) (dual of [(17163, 3), 51348, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁴¹, 19683, F₃, 3, 22) (dual of [(19683, 3), 58908, 23]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using
    - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (119, 141, 3204865)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 797367 340368 918619 275717 812667 334572 927792 086660 912446 547490 240507 > 3¹⁴¹ [i]