MinT - Best Known (29, 29+60, s)-Nets in Base 32

Best Known (29, 29+60, s)-Nets in Base 32

(29, 29+60, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(29, 29+60, 192)-Net in Base 32 — Constructive

(29, 89, 192)-net in base 32, using

2 times m-reduction [i] based on (29, 91, 192)-net in base 32, using
- base change [i] based on digital (3, 65, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(29, 29+60, 257)-Net over F₃₂ — Digital

Digital (29, 89, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 89, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(29, 29+60, 11326)-Net in Base 32 — Upper bound on s

There is no (29, 89, 11327)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 90 868229 256026 661179 854089 060446 306900 395753 085682 596325 209456 473328 408354 139824 963870 984817 310575 295925 427480 185233 555596 517152 872835 > 32⁸⁹ [i]