MinT - Best Known (112, 126, s)-Nets in Base 2

Best Known (112, 126, s)-Nets in Base 2

Digital (112, 126, 37449)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹²⁶, 37449, F₂, 14, 14) (dual of [(37449, 14), 524160, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2¹²⁶, 262143, F₂, 14) (dual of [262143, 262017, 15]-code), using
  - 1 times truncation [i] based on linear OA(2¹²⁷, 262144, F₂, 15) (dual of [262144, 262017, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Digital (112, 126, 52428)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹²⁶, 52428, F₂, 5, 14) (dual of [(52428, 5), 262014, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹²⁶, 262140, F₂, 14) (dual of [262140, 262014, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹²⁶, 262143, F₂, 14) (dual of [262143, 262017, 15]-code), using
    - 1 times truncation [i] based on linear OA(2¹²⁷, 262144, F₂, 15) (dual of [262144, 262017, 16]-code), using
      - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

There is no (112, 126, 886041)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 85 070797 434620 158108 377568 585430 594560 > 2¹²⁶ [i]