MinT - Best Known (85−52, 85, s)-Nets in Base 32

Best Known (85−52, 85, s)-Nets in Base 32

(85−52, 85, 131)-Net over F₃₂ — Constructive and digital

Digital (33, 85, 131)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 26, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
2. digital (7, 59, 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]

(85−52, 85, 257)-Net in Base 32 — Constructive

(33, 85, 257)-net in base 32, using

3 times m-reduction [i] based on (33, 88, 257)-net in base 32, using
- base change [i] based on digital (0, 55, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(85−52, 85, 273)-Net over F₃₂ — Digital

Digital (33, 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]

(85−52, 85, 281)-Net in Base 32

(33, 85, 281)-net in base 32, using

5 times m-reduction [i] based on (33, 90, 281)-net in base 32, using
- base change [i] based on digital (18, 75, 281)-net over F₆₄, using
  - net from sequence [i] based on digital (18, 280)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 18 and N(F) ≥ 281, using
      - a curve from the manYPoints database [i]

(85−52, 85, 28340)-Net in Base 32 — Upper bound on s

There is no (33, 85, 28341)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 86 674643 291348 747592 866389 144122 745652 161652 754572 768678 928319 379998 940068 494241 019153 447375 236549 967520 462353 671566 155330 186600 > 32⁸⁵ [i]