MinT - Best Known (170, 191, s)-Nets in Base 2

Best Known (170, 191, s)-Nets in Base 2

Digital (170, 191, 52428)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁹¹, 52428, F₂, 21, 21) (dual of [(52428, 21), 1100797, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2¹⁹¹, 524281, F₂, 21) (dual of [524281, 524090, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁹¹, 524287, F₂, 21) (dual of [524287, 524096, 22]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [0,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (170, 191, 74898)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁹¹, 74898, F₂, 7, 21) (dual of [(74898, 7), 524095, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2¹⁹¹, 524286, F₂, 21) (dual of [524286, 524095, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁹¹, 524287, F₂, 21) (dual of [524287, 524096, 22]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [0,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (170, 191, 2374344)-net in base 2, because

1 times m-reduction [i] would yield (170, 190, 2374344)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1569 278034 758330 985829 646854 282283 141632 831172 585919 472344 > 2¹⁹⁰ [i]