MinT - Best Known (13, 13+52, s)-Nets in Base 32

Best Known (13, 13+52, s)-Nets in Base 32

(13, 13+52, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 65, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 65, 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]

(13, 13+52, 129)-Net over F₃₂ — Digital

Digital (13, 65, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 65, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(13, 13+52, 1958)-Net in Base 32 — Upper bound on s

There is no (13, 65, 1959)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 69 054352 029831 386231 726622 630902 710269 083276 906243 251700 384332 112917 747921 794166 277575 581910 479100 > 32⁶⁵ [i]