MinT - Best Known (33, 84, s)-Nets in Base 32

Best Known (33, 84, s)-Nets in Base 32

(33, 84, 142)-Net over F₃₂ — Constructive and digital

Digital (33, 84, 142)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 26, 44)-net over F₃₂, using
  - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
2. digital (7, 58, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(33, 84, 273)-Net over F₃₂ — Digital

Digital (33, 84, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 84, 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]

(33, 84, 288)-Net in Base 32 — Constructive

(33, 84, 288)-net in base 32, using

base change [i] based on digital (9, 60, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(33, 84, 315)-Net in Base 32

(33, 84, 315)-net in base 32, using

base change [i] based on digital (19, 70, 315)-net over F₆₄, using
- net from sequence [i] based on digital (19, 314)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 19 and N(F) ≥ 315, using
    - a curve from the manYPoints database [i]

(33, 84, 32598)-Net in Base 32 — Upper bound on s

There is no (33, 84, 32599)-net in base 32, because

1 times m-reduction [i] would yield (33, 83, 32599)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 84677 436838 417763 654781 947224 866951 160036 275347 723911 411280 991301 962032 812719 829186 629343 063853 358801 898059 609739 887435 960880 > 32⁸³ [i]