MinT - Best Known (75−47, 75, s)-Nets in Base 32

Best Known (75−47, 75, s)-Nets in Base 32

(75−47, 75, 120)-Net over F₃₂ — Constructive and digital

Digital (28, 75, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 75, 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]

(75−47, 75, 216)-Net in Base 32 — Constructive

(28, 75, 216)-net in base 32, using

t-expansion [i] based on (27, 75, 216)-net in base 32, using
- 2 times m-reduction [i] based on (27, 77, 216)-net in base 32, using
  - base change [i] based on digital (5, 55, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(75−47, 75, 257)-Net over F₃₂ — Digital

Digital (28, 75, 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]

(75−47, 75, 258)-Net in Base 32

(28, 75, 258)-net in base 32, using

3 times m-reduction [i] based on (28, 78, 258)-net in base 32, using
- base change [i] based on digital (15, 65, 258)-net over F₆₄, using
  - net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
      - a curve from the manYPoints database [i]

(75−47, 75, 21159)-Net in Base 32 — Upper bound on s

There is no (28, 75, 21160)-net in base 32, because

1 times m-reduction [i] would yield (28, 74, 21160)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2405 611330 992750 354065 443255 093399 642670 372523 865780 340794 790769 491860 212615 531525 946724 698180 347946 670859 929738 > 32⁷⁴ [i]