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

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

(47, 47+36, 260)-Net over F₃₂ — Constructive and digital

Digital (47, 83, 260)-net over F₃₂, using

1 times m-reduction [i] based on digital (47, 84, 260)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (3, 15, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
  2. digital (7, 25, 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]
  3. digital (7, 44, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(47, 47+36, 513)-Net in Base 32 — Constructive

(47, 83, 513)-net in base 32, using

t-expansion [i] based on (46, 83, 513)-net in base 32, using
- 25 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+36, 1682)-Net over F₃₂ — Digital

Digital (47, 83, 1682)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+36, 2124126)-Net in Base 32 — Upper bound on s

There is no (47, 83, 2124127)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 84615 809900 987798 459204 312878 878980 494042 137135 001199 269254 005252 061428 770745 354426 590199 169291 331168 321716 794118 473202 066005 > 32⁸³ [i]