MinT - Best Known (90−58, 90, s)-Nets in Base 32

Best Known (90−58, 90, s)-Nets in Base 32

(90−58, 90, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 90, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 90, 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]

(90−58, 90, 216)-Net in Base 32 — Constructive

(32, 90, 216)-net in base 32, using

t-expansion [i] based on (31, 90, 216)-net in base 32, using
- 1 times m-reduction [i] based on (31, 91, 216)-net in base 32, using
  - base change [i] based on digital (5, 65, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(90−58, 90, 273)-Net over F₃₂ — Digital

Digital (32, 90, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 90, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(90−58, 90, 17642)-Net in Base 32 — Upper bound on s

There is no (32, 90, 17643)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2912 099349 738222 649464 041101 465325 133010 950365 541269 161410 221106 171541 193915 937832 674959 314209 397320 232434 354165 575000 973802 573626 464848 > 32⁹⁰ [i]