MinT - Best Known (37, 37+73, s)-Nets in Base 32

Best Known (37, 37+73, s)-Nets in Base 32

(37, 37+73, 120)-Net over F₃₂ — Constructive and digital

Digital (37, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(37, 37+73, 192)-Net in Base 32 — Constructive

(37, 110, 192)-net in base 32, using

32² times duplication [i] based on (35, 108, 192)-net in base 32, using
- t-expansion [i] based on (34, 108, 192)-net in base 32, using
  - base change [i] based on (16, 90, 192)-net in base 64, using
    - 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
      - base change [i] based on digital (3, 78, 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]

(37, 37+73, 273)-Net over F₃₂ — Digital

Digital (37, 110, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 110, 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]

(37, 37+73, 16601)-Net in Base 32 — Upper bound on s

There is no (37, 110, 16602)-net in base 32, because

1 times m-reduction [i] would yield (37, 109, 16602)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 297624 318532 898996 283867 441107 644024 605987 414361 406281 960320 022033 012687 529227 832734 073084 090445 942369 712397 722105 901246 733545 587480 089959 857584 395362 152885 761052 > 32¹⁰⁹ [i]