MinT - Best Known (60, 60+12, s)-Nets in Base 2

Best Known (60, 60+12, s)-Nets in Base 2

Digital (60, 72, 682)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁷², 682, F₂, 12, 12) (dual of [(682, 12), 8112, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2⁷², 4092, F₂, 12) (dual of [4092, 4020, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁷², 4096, F₂, 12) (dual of [4096, 4024, 13]-code), using
    - 1 times truncation [i] based on linear OA(2⁷³, 4097, F₂, 13) (dual of [4097, 4024, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (60, 72, 1365)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁷², 1365, F₂, 3, 12) (dual of [(1365, 3), 4023, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁷², 4095, F₂, 12) (dual of [4095, 4023, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁷², 4096, F₂, 12) (dual of [4096, 4024, 13]-code), using
    - 1 times truncation [i] based on linear OA(2⁷³, 4097, F₂, 13) (dual of [4097, 4024, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (60, 72, 12255)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4724 475173 529438 898547 > 2⁷² [i]