MinT - Best Known (90, 90+12, s)-Nets in Base 2

Best Known (90, 90+12, s)-Nets in Base 2

Digital (90, 102, 21845)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁰², 21845, F₂, 12, 12) (dual of [(21845, 12), 262038, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2¹⁰², 131070, F₂, 12) (dual of [131070, 130968, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁰², 131072, F₂, 12) (dual of [131072, 130970, 13]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁰³, 131073, F₂, 13) (dual of [131073, 130970, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (90, 102, 32768)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁰², 32768, F₂, 4, 12) (dual of [(32768, 4), 130970, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁰², 131072, F₂, 12) (dual of [131072, 130970, 13]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁰³, 131073, F₂, 13) (dual of [131073, 130970, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (90, 102, 392395)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 070662 874650 160947 855090 077370 > 2¹⁰² [i]