MinT - Best Known (104, 203, s)-Nets in Base 2

Best Known (104, 203, s)-Nets in Base 2

Digital (104, 203, 55)-net over F₂, using

t-expansion [i] based on digital (100, 203, 55)-net over F₂, using
- net from sequence [i] based on digital (100, 54)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 6 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

Digital (104, 203, 65)-net over F₂, using

t-expansion [i] based on digital (95, 203, 65)-net over F₂, using
- net from sequence [i] based on digital (95, 64)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 95 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

There is no digital (104, 203, 234)-net over F₂, because

1 times m-reduction [i] would yield digital (104, 202, 234)-net over F₂, but
- extracting embedded orthogonal array [i] would yield linear OA(2²⁰², 234, F₂, 98) (dual of [234, 32, 99]-code), but
  - residual code [i] would yield OA(2¹⁰⁴, 135, S₂, 49), but
    - 1 times truncation [i] would yield OA(2¹⁰³, 134, S₂, 48), but
      - the linear programming bound shows that MÂ â‰¥ 14817 140394 002966 911489 108655 371959 926784 / 1391 278625 > 2¹⁰³ [i]

There is no (104, 203, 267)-net in base 2, because

1 times m-reduction [i] would yield (104, 202, 267)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 002752 860830 517919 539481 172668 989636 712529 615994 155226 304832 > 2²⁰² [i]