MinT - Best Known (37, 109, s)-Nets in Base 32

Best Known (37, 109, s)-Nets in Base 32

(37, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (37, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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, 109, 216)-Net in Base 32 — Constructive

(37, 109, 216)-net in base 32, using

32¹ times duplication [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
    - base change [i] based on digital (5, 78, 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]

(37, 109, 273)-Net over F₃₂ — Digital

Digital (37, 109, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 109, 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, 109, 281)-Net in Base 32

(37, 109, 281)-net in base 32, using

32¹ times duplication [i] based on (36, 108, 281)-net in base 32, using
- base change [i] based on digital (18, 90, 281)-net over F₆₄, using
  - net from sequence [i] based on digital (18, 280)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 18 and N(F) ≥ 281, using
      - a curve from the manYPoints database [i]

(37, 109, 16601)-Net in Base 32 — Upper bound on s

There is no (37, 109, 16602)-net in base 32, because

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]