MinT - Best Known (39, 39+41, s)-Nets in Base 32

Best Known (39, 39+41, s)-Nets in Base 32

(39, 39+41, 218)-Net over F₃₂ — Constructive and digital

Digital (39, 80, 218)-net over F₃₂, using

1 times m-reduction [i] based on digital (39, 81, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 28, 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 (11, 53, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(39, 39+41, 288)-Net in Base 32 — Constructive

(39, 80, 288)-net in base 32, using

25 times m-reduction [i] based on (39, 105, 288)-net in base 32, using
- base change [i] based on digital (9, 75, 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]

(39, 39+41, 539)-Net over F₃₂ — Digital

Digital (39, 80, 539)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+41, 236193)-Net in Base 32 — Upper bound on s

There is no (39, 80, 236194)-net in base 32, because

1 times m-reduction [i] would yield (39, 79, 236194)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80697 401855 215511 511014 654712 808782 744809 823041 655268 128045 872621 171875 540544 031290 655135 131834 147182 490656 694229 652552 > 32⁷⁹ [i]