MinT - Best Known (37, 37+46, s)-Nets in Base 32

Best Known (37, 37+46, s)-Nets in Base 32

(37, 37+46, 196)-Net over F₃₂ — Constructive and digital

Digital (37, 83, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 30, 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 (7, 53, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(37, 37+46, 288)-Net in Base 32 — Constructive

(37, 83, 288)-net in base 32, using

15 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 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]

(37, 37+46, 338)-Net over F₃₂ — Digital

Digital (37, 83, 338)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 37+46, 342)-Net in Base 32

(37, 83, 342)-net in base 32, using

19 times m-reduction [i] based on (37, 102, 342)-net in base 32, using
- base change [i] based on digital (20, 85, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(37, 37+46, 82160)-Net in Base 32 — Upper bound on s

There is no (37, 83, 82161)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 84637 610832 090806 437056 532461 015748 751682 514806 375770 931794 790575 296166 032030 985663 279444 395030 568823 387340 878872 592513 643552 > 32⁸³ [i]