MinT - Best Known (44−31, 44, s)-Nets in Base 32

Best Known (44−31, 44, s)-Nets in Base 32

(44−31, 44, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 44, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 44, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(44−31, 44, 128)-Net in Base 32 — Constructive

(13, 44, 128)-net in base 32, using

4 times m-reduction [i] based on (13, 48, 128)-net in base 32, using
- base change [i] based on digital (5, 40, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(44−31, 44, 129)-Net over F₃₂ — Digital

Digital (13, 44, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 44, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(44−31, 44, 133)-Net in Base 32

(13, 44, 133)-net in base 32, using

4 times m-reduction [i] based on (13, 48, 133)-net in base 32, using
- base change [i] based on digital (5, 40, 133)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
      - a curve from the manYPoints database [i]

(44−31, 44, 4269)-Net in Base 32 — Upper bound on s

There is no (13, 44, 4270)-net in base 32, because

1 times m-reduction [i] would yield (13, 43, 4270)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 52692 273732 883192 206438 743113 750823 991726 810572 956995 503698 198288 > 32⁴³ [i]