MinT - Best Known (36, 36+47, s)-Nets in Base 32

Best Known (36, 36+47, s)-Nets in Base 32

(36, 36+47, 174)-Net over F₃₂ — Constructive and digital

Digital (36, 83, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (36, 84, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 29, 76)-net over F₃₂, using
    - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
        a function field by SÃ©mirat [i]
  2. digital (7, 55, 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]

(36, 36+47, 288)-Net in Base 32 — Constructive

(36, 83, 288)-net in base 32, using

t-expansion [i] based on (35, 83, 288)-net in base 32, using
- 8 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
  - base change [i] based on digital (9, 65, 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]

(36, 36+47, 297)-Net over F₃₂ — Digital

Digital (36, 83, 297)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+47, 342)-Net in Base 32

(36, 83, 342)-net in base 32, using

13 times m-reduction [i] based on (36, 96, 342)-net in base 32, using
- base change [i] based on digital (20, 80, 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]

(36, 36+47, 70665)-Net in Base 32 — Upper bound on s

There is no (36, 83, 70666)-net in base 32, because

1 times m-reduction [i] would yield (36, 82, 70666)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2644 391694 888775 374909 577497 428800 670823 815299 458253 637213 364380 503863 127900 380813 660394 935999 463633 440883 451282 231885 660416 > 32⁸² [i]