MinT - Best Known (55−39, 55, s)-Nets in Base 32

Best Known (55−39, 55, s)-Nets in Base 32

(55−39, 55, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 55, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 55, 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]

(55−39, 55, 129)-Net in Base 32 — Constructive

(16, 55, 129)-net in base 32, using

1 times m-reduction [i] based on (16, 56, 129)-net in base 32, using
- base change [i] based on digital (0, 40, 129)-net over F₁₂₈, using
  - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
      - the rational function field F₁₂₈(x) [i]
    - Niederreiter sequence [i]

(55−39, 55, 158)-Net over F₃₂ — Digital

Digital (16, 55, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 55, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(55−39, 55, 161)-Net in Base 32

(16, 55, 161)-net in base 32, using

5 times m-reduction [i] based on (16, 60, 161)-net in base 32, using
- base change [i] based on digital (6, 50, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(55−39, 55, 4839)-Net in Base 32 — Upper bound on s

There is no (16, 55, 4840)-net in base 32, because

1 times m-reduction [i] would yield (16, 54, 4840)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1901 974630 563379 745635 910020 034005 201804 630030 521973 046656 159662 834164 989667 975738 > 32⁵⁴ [i]