MinT - Best Known (105−59, 105, s)-Nets in Base 32

Best Known (105−59, 105, s)-Nets in Base 32

(105−59, 105, 202)-Net over F₃₂ — Constructive and digital

Digital (46, 105, 202)-net over F₃₂, using

1 times m-reduction [i] based on digital (46, 106, 202)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 37, 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, 69, 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]

(105−59, 105, 375)-Net over F₃₂ — Digital

Digital (46, 105, 375)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−59, 105, 513)-Net in Base 32 — Constructive

(46, 105, 513)-net in base 32, using

3 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]

(105−59, 105, 94074)-Net in Base 32 — Upper bound on s

There is no (46, 105, 94075)-net in base 32, because

1 times m-reduction [i] would yield (46, 104, 94075)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 433224 345520 993809 133382 321530 261779 866823 098635 316058 248315 417611 202569 710254 478539 629779 028020 121837 538853 575870 048933 508550 131163 503819 180568 062237 033264 > 32¹⁰⁴ [i]