MinT - Best Known (22, 22+88, s)-Nets in Base 32

Best Known (22, 22+88, s)-Nets in Base 32

(22, 22+88, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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+88, 185)-Net over F₃₂ — Digital

Digital (22, 110, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 110, 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+88, 3201)-Net in Base 32 — Upper bound on s

There is no (22, 110, 3202)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3714 832289 177988 339906 516226 117315 622792 597605 319902 456130 539852 273510 122054 505551 978714 491287 438906 462877 109493 686915 227616 753600 546019 906605 727473 652022 868231 557280 > 32¹¹⁰ [i]