MinT - Best Known (85, 85+10, s)-Nets in Base 2

Best Known (85, 85+10, s)-Nets in Base 2

Digital (85, 95, 104857)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁹⁵, 104857, F₂, 10, 10) (dual of [(104857, 10), 1048475, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2⁹⁵, 524285, F₂, 10) (dual of [524285, 524190, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹⁵, 524287, F₂, 10) (dual of [524287, 524192, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using
      - an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Digital (85, 95, 131071)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁹⁵, 131071, F₂, 4, 10) (dual of [(131071, 4), 524189, 11]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁹⁵, 524284, F₂, 10) (dual of [524284, 524189, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹⁵, 524287, F₂, 10) (dual of [524287, 524192, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using
      - an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

There is no (85, 95, 1365853)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 39614 090296 047216 482822 124342 > 2⁹⁵ [i]