MinT - Best Known (198, 220, s)-Nets in Base 2

Best Known (198, 220, s)-Nets in Base 2

Digital (198, 220, 95325)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²²⁰, 95325, F₂, 22, 22) (dual of [(95325, 22), 2096930, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2²²⁰, 1048575, F₂, 22) (dual of [1048575, 1048355, 23]-code), using
  - 1 times truncation [i] based on linear OA(2²²¹, 1048576, F₂, 23) (dual of [1048576, 1048355, 24]-code), using
    - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Digital (198, 220, 149796)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²²⁰, 149796, F₂, 7, 22) (dual of [(149796, 7), 1048352, 23]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2²²⁰, 1048572, F₂, 22) (dual of [1048572, 1048352, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²²⁰, 1048575, F₂, 22) (dual of [1048575, 1048355, 23]-code), using
    - 1 times truncation [i] based on linear OA(2²²¹, 1048576, F₂, 23) (dual of [1048576, 1048355, 24]-code), using
      - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

There is no (198, 220, 5147694)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 684996 801490 468872 881472 235307 528309 929610 918223 519471 704017 740550 > 2²²⁰ [i]