MinT - Best Known (47, 47+53, s)-Nets in Base 32

Best Known (47, 47+53, s)-Nets in Base 32

(47, 47+53, 224)-Net over F₃₂ — Constructive and digital

Digital (47, 100, 224)-net over F₃₂, using

1 times m-reduction [i] based on digital (47, 101, 224)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 36, 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]
  2. digital (11, 65, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(47, 47+53, 513)-Net in Base 32 — Constructive

(47, 100, 513)-net in base 32, using

t-expansion [i] based on (46, 100, 513)-net in base 32, using
- 8 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 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]

(47, 47+53, 513)-Net over F₃₂ — Digital

Digital (47, 100, 513)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+53, 183251)-Net in Base 32 — Upper bound on s

There is no (47, 100, 183252)-net in base 32, because

1 times m-reduction [i] would yield (47, 99, 183252)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102299 539847 254514 888538 028361 844143 520985 961704 951309 517944 852320 162527 869137 727170 191992 728224 291014 041403 044018 978750 049115 392178 647552 924976 894056 > 32⁹⁹ [i]