MinT - Best Known (180, 180+21, s)-Nets in Base 2

Best Known (180, 180+21, s)-Nets in Base 2

Digital (180, 201, 104857)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁰¹, 104857, F₂, 21, 21) (dual of [(104857, 21), 2201796, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2²⁰¹, 1048571, F₂, 21) (dual of [1048571, 1048370, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰¹, 1048576, F₂, 21) (dual of [1048576, 1048375, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Digital (180, 201, 149796)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁰¹, 149796, F₂, 7, 21) (dual of [(149796, 7), 1048371, 22]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2²⁰¹, 1048572, F₂, 21) (dual of [1048572, 1048371, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰¹, 1048576, F₂, 21) (dual of [1048576, 1048375, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

There is no (180, 201, 4748702)-net in base 2, because

1 times m-reduction [i] would yield (180, 200, 4748702)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 606939 015821 007457 331120 625317 637385 527703 835820 210923 724434 > 2²⁰⁰ [i]