MinT - Best Known (75−10, 75, s)-Nets in Base 2

Best Known (75−10, 75, s)-Nets in Base 2

Digital (65, 75, 6553)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁷⁵, 6553, F₂, 10, 10) (dual of [(6553, 10), 65455, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2⁷⁵, 32765, F₂, 10) (dual of [32765, 32690, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁷⁵, 32767, F₂, 10) (dual of [32767, 32692, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁷⁶, 32768, F₂, 11) (dual of [32768, 32692, 12]-code), using
      - an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Digital (65, 75, 10922)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁷⁵, 10922, F₂, 3, 10) (dual of [(10922, 3), 32691, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁷⁵, 32766, F₂, 10) (dual of [32766, 32691, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁷⁵, 32767, F₂, 10) (dual of [32767, 32692, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁷⁶, 32768, F₂, 11) (dual of [32768, 32692, 12]-code), using
      - an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

There is no (65, 75, 85360)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 37780 599537 274517 748573 > 2⁷⁵ [i]