MinT - Best Known (126, 126+19, s)-Nets in Base 2

Best Known (126, 126+19, s)-Nets in Base 2

Digital (126, 145, 7281)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁴⁵, 7281, F₂, 19, 19) (dual of [(7281, 19), 138194, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2¹⁴⁵, 65530, F₂, 19) (dual of [65530, 65385, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁴⁵, 65536, F₂, 19) (dual of [65536, 65391, 20]-code), using
    - an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Digital (126, 145, 10922)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁴⁵, 10922, F₂, 6, 19) (dual of [(10922, 6), 65387, 20]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2¹⁴⁵, 65532, F₂, 19) (dual of [65532, 65387, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁴⁵, 65536, F₂, 19) (dual of [65536, 65391, 20]-code), using
    - an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

There is no (126, 145, 271776)-net in base 2, because

1 times m-reduction [i] would yield (126, 144, 271776)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 300974 688195 888357 527194 969127 337851 214117 > 2¹⁴⁴ [i]