MinT - Best Known (92−67, 92, s)-Nets in Base 4

Best Known (92−67, 92, s)-Nets in Base 4

Digital (25, 92, 34)-net over F₄, using

(25, 92, 35)-net in base 4, using

t-expansion [i] based on (24, 92, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
  - base expansion [i] based on digital (48, 34)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 41, N(F)Â =Â 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F₂ with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

Digital (25, 92, 51)-net over F₄, using

There is no (25, 92, 111)-net in base 4, because

1 times m-reduction [i] would yield (25, 91, 111)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(4⁹¹, 111, S₄, 66), but
  - the linear programming bound shows that MÂ â‰¥ 55 370157 580736 154116 963294 828751 876036 101137 474368 823948 817345 806336 / 8 191907 762077 > 4⁹¹ [i]