MinT - Best Known (102, 114, s)-Nets in Base 2

Best Known (102, 114, s)-Nets in Base 2

Digital (102, 114, 87381)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹¹⁴, 87381, F₂, 12, 12) (dual of [(87381, 12), 1048458, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2¹¹⁴, 524286, F₂, 12) (dual of [524286, 524172, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹¹⁴, 524288, F₂, 12) (dual of [524288, 524174, 13]-code), using
    - 1 times truncation [i] based on linear OA(2¹¹⁵, 524289, F₂, 13) (dual of [524289, 524174, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 524289Â | 2³⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (102, 114, 131072)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹¹⁴, 131072, F₂, 4, 12) (dual of [(131072, 4), 524174, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹¹⁴, 524288, F₂, 12) (dual of [524288, 524174, 13]-code), using
  - 1 times truncation [i] based on linear OA(2¹¹⁵, 524289, F₂, 13) (dual of [524289, 524174, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 524289Â | 2³⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (102, 114, 1569603)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20769 236676 332356 056484 013855 397568 > 2¹¹⁴ [i]