MinT - Best Known (38, 38+45, s)-Nets in Base 32

Best Known (38, 38+45, s)-Nets in Base 32

(38, 38+45, 202)-Net over F₃₂ — Constructive and digital

Digital (38, 83, 202)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 29, 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 (9, 54, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(38, 38+45, 288)-Net in Base 32 — Constructive

(38, 83, 288)-net in base 32, using

t-expansion [i] based on (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]

(38, 38+45, 386)-Net over F₃₂ — Digital

Digital (38, 83, 386)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+45, 119002)-Net in Base 32 — Upper bound on s

There is no (38, 83, 119003)-net in base 32, because

1 times m-reduction [i] would yield (38, 82, 119003)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2644 628214 439980 436096 109651 280168 440445 764188 304847 941180 659254 082913 476757 137515 603697 451050 808987 498787 768752 054095 721838 > 32⁸² [i]