MinT - Best Known (13, 13+22, s)-Nets in Base 32

Best Known (13, 13+22, s)-Nets in Base 32

(13, 13+22, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 35, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 35, 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+22, 129)-Net over F₃₂ — Digital

Digital (13, 35, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 35, 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+22, 192)-Net in Base 32 — Constructive

(13, 35, 192)-net in base 32, using

base change [i] based on digital (3, 25, 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]

(13, 13+22, 9739)-Net in Base 32 — Upper bound on s

There is no (13, 35, 9740)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 47928 826531 940206 918711 379601 085946 070473 464547 260223 > 32³⁵ [i]