MinT - Best Known (190, 190+21, s)-Nets in Base 2

Best Known (190, 190+21, s)-Nets in Base 2

Digital (190, 211, 209715)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²¹¹, 209715, F₂, 21, 21) (dual of [(209715, 21), 4403804, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2²¹¹, 2097151, F₂, 21) (dual of [2097151, 2096940, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹¹, 2097152, F₂, 21) (dual of [2097152, 2096941, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Digital (190, 211, 299593)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²¹¹, 299593, F₂, 7, 21) (dual of [(299593, 7), 2096940, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2²¹¹, 2097151, F₂, 21) (dual of [2097151, 2096940, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹¹, 2097152, F₂, 21) (dual of [2097152, 2096941, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

There is no (190, 211, large)-net in base 2, because

19 times m-reduction [i] would yield (190, 192, large)-net in base 2, but
- mutually orthogonal hypercube bound [i]