MinT - Best Known (110−66, 110, s)-Nets in Base 32

Best Known (110−66, 110, s)-Nets in Base 32

(110−66, 110, 162)-Net over F₃₂ — Constructive and digital

Digital (44, 110, 162)-net over F₃₂, using

t-expansion [i] based on digital (43, 110, 162)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (3, 36, 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, 74, 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]

(110−66, 110, 288)-Net in Base 32 — Constructive

(44, 110, 288)-net in base 32, using

32² times duplication [i] based on (42, 108, 288)-net in base 32, using
- t-expansion [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
        net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(110−66, 110, 325)-Net over F₃₂ — Digital

Digital (44, 110, 325)-net over F₃₂, using

net from sequence [i] based on digital (44, 324)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 44 and N(F) ≥ 325, using
  - a curve from the manYPoints database [i]

(110−66, 110, 342)-Net in Base 32

(44, 110, 342)-net in base 32, using

32² times duplication [i] based on (42, 108, 342)-net in base 32, using
- t-expansion [i] based on (38, 108, 342)-net in base 32, using
  - base change [i] based on digital (20, 90, 342)-net over F₆₄, using
    - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
        a curve from the manYPoints database [i]

(110−66, 110, 44156)-Net in Base 32 — Upper bound on s

There is no (44, 110, 44157)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3687 845045 146366 649303 532308 958957 620651 918752 852208 501371 974988 871668 848661 341905 150988 183332 130640 139588 201836 773773 520383 873362 526630 105554 224286 762125 535430 746580 > 32¹¹⁰ [i]