MinT - Best Known (132, 132+25, s)-Nets in Base 2

Best Known (132, 132+25, s)-Nets in Base 2

Digital (132, 157, 682)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁵⁷, 682, F₂, 25, 25) (dual of [(682, 25), 16893, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2¹⁵⁷, 8185, F₂, 25) (dual of [8185, 8028, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁵⁷, 8192, F₂, 25) (dual of [8192, 8035, 26]-code), using
    - an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]

Digital (132, 157, 1639)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁵⁷, 1639, F₂, 4, 25) (dual of [(1639, 4), 6399, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁵⁷, 2048, F₂, 4, 25) (dual of [(2048, 4), 8035, 26]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁵⁷, 8192, F₂, 25) (dual of [8192, 8035, 26]-code), using
    - an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]

There is no (132, 157, 43309)-net in base 2, because

1 times m-reduction [i] would yield (132, 156, 43309)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91349 450750 406918 701825 053654 929259 562820 174037 > 2¹⁵⁶ [i]