MinT - Best Known (47, 108, s)-Nets in Base 32

Best Known (47, 108, s)-Nets in Base 32

(47, 108, 202)-Net over F₃₂ — Constructive and digital

Digital (47, 108, 202)-net over F₃₂, using

1 times m-reduction [i] based on digital (47, 109, 202)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 38, 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, 71, 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]

(47, 108, 372)-Net over F₃₂ — Digital

Digital (47, 108, 372)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 108, 513)-Net in Base 32 — Constructive

(47, 108, 513)-net in base 32, using

t-expansion [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, 108, 90723)-Net in Base 32 — Upper bound on s

There is no (47, 108, 90724)-net in base 32, because

1 times m-reduction [i] would yield (47, 107, 90724)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112480 563065 857210 525666 471550 401933 280897 867210 152525 309646 208049 251329 787501 525513 253088 225152 982063 277829 193869 090796 683530 609566 449323 034155 747691 982934 217320 > 32¹⁰⁷ [i]