MinT - Best Known (104, 130, s)-Nets in Base 2

Best Known (104, 130, s)-Nets in Base 2

Digital (104, 130, 260)-net over F₂, using

2² times duplication [i] based on digital (102, 128, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 32, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

Digital (104, 130, 414)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹³⁰, 414, F₂, 2, 26) (dual of [(414, 2), 698, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹³⁰, 511, F₂, 2, 26) (dual of [(511, 2), 892, 27]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁰, 1022, F₂, 26) (dual of [1022, 892, 27]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁰, 1023, F₂, 26) (dual of [1023, 893, 27]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

There is no (104, 130, 5785)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1361 910797 431663 438719 452405 762978 703688 > 2¹³⁰ [i]