MinT - Best Known (84, 84+12, s)-Nets in Base 2

Best Known (84, 84+12, s)-Nets in Base 2

Digital (84, 96, 10922)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁹⁶, 10922, F₂, 12, 12) (dual of [(10922, 12), 130968, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2⁹⁶, 65532, F₂, 12) (dual of [65532, 65436, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹⁶, 65536, F₂, 12) (dual of [65536, 65440, 13]-code), using
    - 1 times truncation [i] based on linear OA(2⁹⁷, 65537, F₂, 13) (dual of [65537, 65440, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (84, 96, 16384)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁹⁶, 16384, F₂, 4, 12) (dual of [(16384, 4), 65440, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁹⁶, 65536, F₂, 12) (dual of [65536, 65440, 13]-code), using
  - 1 times truncation [i] based on linear OA(2⁹⁷, 65537, F₂, 13) (dual of [65537, 65440, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (84, 96, 196193)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 79228 501405 269736 098499 953040 > 2⁹⁶ [i]