MinT - Best Known (45, 45+57, s)-Nets in Base 32

Best Known (45, 45+57, s)-Nets in Base 32

(45, 45+57, 202)-Net over F₃₂ — Constructive and digital

Digital (45, 102, 202)-net over F₃₂, using

1 times m-reduction [i] based on digital (45, 103, 202)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 36, 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, 67, 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]

(45, 45+57, 378)-Net over F₃₂ — Digital

Digital (45, 102, 378)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+57, 513)-Net in Base 32 — Constructive

(45, 102, 513)-net in base 32, using

base change [i] based on digital (28, 85, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(45, 45+57, 97919)-Net in Base 32 — Upper bound on s

There is no (45, 102, 97920)-net in base 32, because

1 times m-reduction [i] would yield (45, 101, 97920)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 104 754918 337058 680855 965693 063635 715279 409857 424598 031582 893449 289320 755021 609337 667115 514881 872192 955955 282345 525389 361750 875513 183747 312574 853893 874713 > 32¹⁰¹ [i]