MinT - Best Known (35, 35+56, s)-Nets in Base 32

Best Known (35, 35+56, s)-Nets in Base 32

(35, 35+56, 131)-Net over F₃₂ — Constructive and digital

Digital (35, 91, 131)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 28, 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, 63, 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]

(35, 35+56, 273)-Net over F₃₂ — Digital

Digital (35, 91, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 91, 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]

(35, 35+56, 288)-Net in Base 32 — Constructive

(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]

(35, 35+56, 315)-Net in Base 32

(35, 91, 315)-net in base 32, using

5 times m-reduction [i] based on (35, 96, 315)-net in base 32, using
- base change [i] based on digital (19, 80, 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]

(35, 35+56, 28389)-Net in Base 32 — Upper bound on s

There is no (35, 91, 28390)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93064 631440 795192 647546 846896 041481 784188 533588 614140 856313 463797 036113 301432 970131 890996 867358 773861 071750 717605 785820 043660 147104 326252 > 32⁹¹ [i]