MinT - Best Known (85−57, 85, s)-Nets in Base 32

Best Known (85−57, 85, s)-Nets in Base 32

(85−57, 85, 120)-Net over F₃₂ — Constructive and digital

Digital (28, 85, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 85, 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]

(85−57, 85, 192)-Net in Base 32 — Constructive

(28, 85, 192)-net in base 32, using

32¹ times duplication [i] based on (27, 84, 192)-net in base 32, using
- base change [i] based on digital (3, 60, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(85−57, 85, 257)-Net over F₃₂ — Digital

Digital (28, 85, 257)-net over F₃₂, using

net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
  - a curve from the manYPoints database [i]

(85−57, 85, 11928)-Net in Base 32 — Upper bound on s

There is no (28, 85, 11929)-net in base 32, because

1 times m-reduction [i] would yield (28, 84, 11929)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 713747 333785 790631 380896 316025 929203 685911 496862 594580 998692 316975 149373 941581 060321 909369 279409 012244 264910 730704 591741 286432 > 32⁸⁴ [i]