MinT - Best Known (22, 22+58, s)-Nets in Base 32

Best Known (22, 22+58, s)-Nets in Base 32

(22, 22+58, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 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]

(22, 22+58, 177)-Net in Base 32 — Constructive

(22, 80, 177)-net in base 32, using

10 times m-reduction [i] based on (22, 90, 177)-net in base 32, using
- base change [i] based on digital (7, 75, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(22, 22+58, 185)-Net over F₃₂ — Digital

Digital (22, 80, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 80, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(22, 22+58, 5329)-Net in Base 32 — Upper bound on s

There is no (22, 80, 5330)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 589765 712479 419803 937314 327343 426548 450811 852169 341608 703304 974838 069437 029859 738815 038144 126819 249571 364706 876265 379120 > 32⁸⁰ [i]