MinT - Best Known (34, 34+61, s)-Nets in Base 32

Best Known (34, 34+61, s)-Nets in Base 32

(34, 34+61, 120)-Net over F₃₂ — Constructive and digital

Digital (34, 95, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 95, 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]

(34, 34+61, 216)-Net in Base 32 — Constructive

(34, 95, 216)-net in base 32, using

t-expansion [i] based on (33, 95, 216)-net in base 32, using
- 3 times m-reduction [i] based on (33, 98, 216)-net in base 32, using
  - base change [i] based on digital (5, 70, 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]

(34, 34+61, 273)-Net over F₃₂ — Digital

Digital (34, 95, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 95, 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]

(34, 34+61, 281)-Net in Base 32

(34, 95, 281)-net in base 32, using

1 times m-reduction [i] based on (34, 96, 281)-net in base 32, using
- base change [i] based on digital (18, 80, 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]

(34, 34+61, 20194)-Net in Base 32 — Upper bound on s

There is no (34, 95, 20195)-net in base 32, because

1 times m-reduction [i] would yield (34, 94, 20195)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3051 265691 843947 453560 096583 337554 439658 704553 658373 889239 687250 615056 992691 434347 523126 076927 238881 176195 460836 302739 541035 895873 368487 507000 > 32⁹⁴ [i]