MinT - Best Known (43, 43+61, s)-Nets in Base 32

Best Known (43, 43+61, s)-Nets in Base 32

(43, 43+61, 174)-Net over F₃₂ — Constructive and digital

Digital (43, 104, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (43, 105, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 36, 76)-net over F₃₂, using
    - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
        a function field by SÃ©mirat [i]
  2. digital (7, 69, 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]

(43, 43+61, 288)-Net in Base 32 — Constructive

(43, 104, 288)-net in base 32, using

t-expansion [i] based on (40, 104, 288)-net in base 32, using
- 4 times m-reduction [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]

(43, 43+61, 308)-Net over F₃₂ — Digital

Digital (43, 104, 308)-net over F₃₂, using

t-expansion [i] based on digital (41, 104, 308)-net over F₃₂, using
- net from sequence [i] based on digital (41, 307)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 41 and N(F) ≥ 308, using
    - a curve from the manYPoints database [i]

(43, 43+61, 408)-Net in Base 32

(43, 104, 408)-net in base 32, using

4 times m-reduction [i] based on (43, 108, 408)-net in base 32, using
- base change [i] based on digital (25, 90, 408)-net over F₆₄, using
  - net from sequence [i] based on digital (25, 407)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 25 and N(F) ≥ 408, using
      - a curve from the manYPoints database [i]

(43, 43+61, 57146)-Net in Base 32 — Upper bound on s

There is no (43, 104, 57147)-net in base 32, because

1 times m-reduction [i] would yield (43, 103, 57147)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107280 209314 638726 760788 307534 941489 423063 646679 169389 087642 359674 936651 068069 633246 938036 948244 425732 350948 080007 157076 744091 633579 488950 639887 020955 625992 > 32¹⁰³ [i]