MinT - Best Known (103−59, 103, s)-Nets in Base 32

Best Known (103−59, 103, s)-Nets in Base 32

(103−59, 103, 196)-Net over F₃₂ — Constructive and digital

Digital (44, 103, 196)-net over F₃₂, using

1 times m-reduction [i] based on digital (44, 104, 196)-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 (7, 67, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(103−59, 103, 288)-Net in Base 32 — Constructive

(44, 103, 288)-net in base 32, using

t-expansion [i] based on (40, 103, 288)-net in base 32, using
- 5 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]

(103−59, 103, 330)-Net over F₃₂ — Digital

Digital (44, 103, 330)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−59, 103, 425)-Net in Base 32

(44, 103, 425)-net in base 32, using

5 times m-reduction [i] based on (44, 108, 425)-net in base 32, using
- base change [i] based on digital (26, 90, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(103−59, 103, 74071)-Net in Base 32 — Upper bound on s

There is no (44, 103, 74072)-net in base 32, because

1 times m-reduction [i] would yield (44, 102, 74072)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3353 184818 835046 921360 183825 736635 670081 032287 161039 907376 934217 759926 730990 931489 842753 969810 998820 574448 305121 442464 324440 209065 526412 476190 742350 709832 > 32¹⁰² [i]