MinT - Best Known (119, 119+15, s)-Nets in Base 2

Best Known (119, 119+15, s)-Nets in Base 2

Digital (119, 134, 74898)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹³⁴, 74898, F₂, 15, 15) (dual of [(74898, 15), 1123336, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2¹³⁴, 524287, F₂, 15) (dual of [524287, 524153, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁴, 524288, F₂, 15) (dual of [524288, 524154, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Digital (119, 134, 87381)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹³⁴, 87381, F₂, 6, 15) (dual of [(87381, 6), 524152, 16]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2¹³⁴, 524286, F₂, 15) (dual of [524286, 524152, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁴, 524288, F₂, 15) (dual of [524288, 524154, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

There is no (119, 134, 1772092)-net in base 2, because

1 times m-reduction [i] would yield (119, 133, 1772092)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10889 062074 835304 816644 067412 360121 123370 > 2¹³³ [i]