MinT - Best Known (85−50, 85, s)-Nets in Base 32

Best Known (85−50, 85, s)-Nets in Base 32

(85−50, 85, 162)-Net over F₃₂ — Constructive and digital

Digital (35, 85, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 28, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (7, 57, 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]

(85−50, 85, 273)-Net over F₃₂ — Digital

Digital (35, 85, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 85, 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]

(85−50, 85, 288)-Net in Base 32 — Constructive

(35, 85, 288)-net in base 32, using

6 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
- base change [i] based on digital (9, 65, 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]

(85−50, 85, 342)-Net in Base 32

(35, 85, 342)-net in base 32, using

5 times m-reduction [i] based on (35, 90, 342)-net in base 32, using
- base change [i] based on digital (20, 75, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(85−50, 85, 43017)-Net in Base 32 — Upper bound on s

There is no (35, 85, 43018)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 86 672952 430821 201206 988641 540554 461333 059839 141872 166878 228555 661688 998641 684674 328133 659870 158602 713903 289907 328863 806395 327872 > 32⁸⁵ [i]