MinT - Best Known (105−69, 105, s)-Nets in Base 32

Best Known (105−69, 105, s)-Nets in Base 32

(105−69, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (36, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(105−69, 105, 216)-Net in Base 32 — Constructive

(36, 105, 216)-net in base 32, using

3 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
    - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(105−69, 105, 273)-Net over F₃₂ — Digital

Digital (36, 105, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 105, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(105−69, 105, 281)-Net in Base 32

(36, 105, 281)-net in base 32, using

3 times m-reduction [i] based on (36, 108, 281)-net in base 32, using
- base change [i] based on digital (18, 90, 281)-net over F₆₄, using
  - net from sequence [i] based on digital (18, 280)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 18 and N(F) ≥ 281, using
      - a curve from the manYPoints database [i]

(105−69, 105, 17525)-Net in Base 32 — Upper bound on s

There is no (36, 105, 17526)-net in base 32, because

1 times m-reduction [i] would yield (36, 104, 17526)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 436872 612393 571053 707338 341052 957932 790936 624011 952408 613532 238674 650688 222982 229900 902463 879295 785289 947398 777063 793311 903111 850707 566898 817454 602520 777426 > 32¹⁰⁴ [i]