MinT - Best Known (107−63, 107, s)-Nets in Base 32

Best Known (107−63, 107, s)-Nets in Base 32

(107−63, 107, 174)-Net over F₃₂ — Constructive and digital

Digital (44, 107, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (44, 108, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 37, 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, 71, 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]

(107−63, 107, 288)-Net in Base 32 — Constructive

(44, 107, 288)-net in base 32, using

t-expansion [i] based on (40, 107, 288)-net in base 32, using
- 1 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]

(107−63, 107, 325)-Net over F₃₂ — Digital

Digital (44, 107, 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]

(107−63, 107, 425)-Net in Base 32

(44, 107, 425)-net in base 32, using

1 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]

(107−63, 107, 56129)-Net in Base 32 — Upper bound on s

There is no (44, 107, 56130)-net in base 32, because

1 times m-reduction [i] would yield (44, 106, 56130)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3516 203196 635684 929819 092162 883346 657897 987029 925320 633617 173585 431491 468546 597846 771302 782762 662802 978959 783947 946027 155258 537549 721978 136723 306757 049301 741344 > 32¹⁰⁶ [i]