MinT - Best Known (105, 105+15, s)-Nets in Base 2

Best Known (105, 105+15, s)-Nets in Base 2

Digital (105, 120, 18724)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹²⁰, 18724, F₂, 15, 15) (dual of [(18724, 15), 280740, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2¹²⁰, 131069, F₂, 15) (dual of [131069, 130949, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹²⁰, 131072, F₂, 15) (dual of [131072, 130952, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Digital (105, 120, 26214)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹²⁰, 26214, F₂, 5, 15) (dual of [(26214, 5), 130950, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹²⁰, 131070, F₂, 15) (dual of [131070, 130950, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹²⁰, 131072, F₂, 15) (dual of [131072, 130952, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

There is no (105, 120, 443016)-net in base 2, because

1 times m-reduction [i] would yield (105, 119, 443016)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 664620 854804 661904 954338 004213 982815 > 2¹¹⁹ [i]