MinT - Best Known (27, 106, s)-Nets in Base 32

Best Known (27, 106, s)-Nets in Base 32

(27, 106, 120)-Net over F₃₂ — Constructive and digital

Digital (27, 106, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 106, 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]

(27, 106, 177)-Net in Base 32 — Constructive

(27, 106, 177)-net in base 32, using

t-expansion [i] based on (25, 106, 177)-net in base 32, using
- 2 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
  - base change [i] based on digital (7, 90, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(27, 106, 225)-Net over F₃₂ — Digital

Digital (27, 106, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 106, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(27, 106, 5582)-Net in Base 32 — Upper bound on s

There is no (27, 106, 5583)-net in base 32, because

1 times m-reduction [i] would yield (27, 105, 5583)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 110 320927 819694 940609 785837 183664 410757 149451 769705 366600 205913 784311 828914 911575 146903 074573 819872 266608 466309 259221 140379 531559 186019 747232 378807 946489 838640 > 32¹⁰⁵ [i]