MinT - Best Known (45, 107, s)-Nets in Base 32

Best Known (45, 107, s)-Nets in Base 32

(45, 107, 196)-Net over F₃₂ — Constructive and digital

Digital (45, 107, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 38, 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]
2. digital (7, 69, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(45, 107, 288)-Net in Base 32 — Constructive

(45, 107, 288)-net in base 32, using

t-expansion [i] based on (40, 107, 288)-net in base 32, using
- 1 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 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]

(45, 107, 325)-Net over F₃₂ — Digital

Digital (45, 107, 325)-net over F₃₂, using

t-expansion [i] based on digital (44, 107, 325)-net over F₃₂, using
- net from sequence [i] based on digital (44, 324)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 44 and N(F) ≥ 325, using
    - a curve from the manYPoints database [i]

(45, 107, 425)-Net in Base 32

(45, 107, 425)-net in base 32, using

t-expansion [i] based on (44, 107, 425)-net in base 32, using
- 1 times m-reduction [i] based on (44, 108, 425)-net in base 32, using
  - base change [i] based on digital (26, 90, 425)-net over F₆₄, using
    - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
        a curve from the manYPoints database [i]

(45, 107, 62770)-Net in Base 32 — Upper bound on s

There is no (45, 107, 62771)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112499 933191 146937 212076 812068 451184 536345 060895 943935 358592 490155 985108 343972 911348 237144 377616 212558 339827 233356 896312 698185 039045 804020 224390 291739 828620 317024 > 32¹⁰⁷ [i]