MinT - Best Known (38, 38+43, s)-Nets in Base 32

Best Known (38, 38+43, s)-Nets in Base 32

(38, 38+43, 202)-Net over F₃₂ — Constructive and digital

Digital (38, 81, 202)-net over F₃₂, using

1 times m-reduction [i] based on digital (38, 82, 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, 53, 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+43, 288)-Net in Base 32 — Constructive

(38, 81, 288)-net in base 32, using

t-expansion [i] based on (37, 81, 288)-net in base 32, using
- 17 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+43, 433)-Net over F₃₂ — Digital

Digital (38, 81, 433)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+43, 151706)-Net in Base 32 — Upper bound on s

There is no (38, 81, 151707)-net in base 32, because

1 times m-reduction [i] would yield (38, 80, 151707)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 582328 852200 222753 814690 502394 282589 200953 125655 973363 561489 504554 988251 372482 745193 571418 588094 356836 148474 503417 137324 > 32⁸⁰ [i]