MinT - Best Known (44, 93, s)-Nets in Base 2

Best Known (44, 93, s)-Nets in Base 2

(44, 93, 33)-Net over F₂ — Constructive and digital

Digital (44, 93, 33)-net over F₂, using

t-expansion [i] based on digital (39, 93, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(44, 93, 34)-Net over F₂ — Digital

Digital (44, 93, 34)-net over F₂, using

t-expansion [i] based on digital (43, 93, 34)-net over F₂, using
- net from sequence [i] based on digital (43, 33)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
    - a curve from the manYPoints database [i]

(44, 93, 96)-Net over F₂ — Upper bound on s (digital)

There is no digital (44, 93, 97)-net over F₂, because

1 times m-reduction [i] would yield digital (44, 92, 97)-net over F₂, but
- extracting embedded orthogonal array [i] would yield linear OA(2⁹², 97, F₂, 48) (dual of [97, 5, 49]-code), but
  - Griesmer bound [i]

(44, 93, 99)-Net in Base 2 — Upper bound on s

There is no (44, 93, 100)-net in base 2, because

3 times m-reduction [i] would yield (44, 90, 100)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2⁹⁰, 100, S₂, 46), but
  - the linear programming bound shows that MÂ â‰¥ 1 861861 819085 211933 448282 832896 / 1305 > 2⁹⁰ [i]