MinT - Best Known (108−64, 108, s)-Nets in Base 32

Best Known (108−64, 108, s)-Nets in Base 32

(108−64, 108, 174)-Net over F₃₂ — Constructive and digital

Digital (44, 108, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 37, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 71, 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]

(108−64, 108, 288)-Net in Base 32 — Constructive

(44, 108, 288)-net in base 32, using

t-expansion [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]

(108−64, 108, 325)-Net over F₃₂ — Digital

Digital (44, 108, 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]

(108−64, 108, 425)-Net in Base 32

(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]

(108−64, 108, 49574)-Net in Base 32 — Upper bound on s

There is no (44, 108, 49575)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 601164 747168 188240 190624 389546 927337 979084 948969 698005 038415 723259 193873 743767 874646 647337 027978 448221 994207 513259 652287 113878 223980 911465 345988 147334 594190 337549 > 32¹⁰⁸ [i]