MinT - Best Known (130, 130+21, s)-Nets in Base 2

Best Known (130, 130+21, s)-Nets in Base 2

Digital (130, 151, 3276)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁵¹, 3276, F₂, 21, 21) (dual of [(3276, 21), 68645, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2¹⁵¹, 32761, F₂, 21) (dual of [32761, 32610, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁵¹, 32768, F₂, 21) (dual of [32768, 32617, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Digital (130, 151, 5461)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁵¹, 5461, F₂, 6, 21) (dual of [(5461, 6), 32615, 22]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2¹⁵¹, 32766, F₂, 21) (dual of [32766, 32615, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁵¹, 32768, F₂, 21) (dual of [32768, 32617, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

There is no (130, 151, 148383)-net in base 2, because

1 times m-reduction [i] would yield (130, 150, 148383)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1427 259014 131262 422386 990080 127194 052494 182083 > 2¹⁵⁰ [i]