MinT - Best Known (13, 36, s)-Nets in Base 32

Best Known (13, 36, s)-Nets in Base 32

(13, 36, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 36, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 36, 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, 36, 129)-Net over F₃₂ — Digital

Digital (13, 36, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 36, 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, 36, 177)-Net in Base 32 — Constructive

(13, 36, 177)-net in base 32, using

base change [i] based on digital (7, 30, 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]

(13, 36, 9739)-Net in Base 32 — Upper bound on s

There is no (13, 36, 9740)-net in base 32, because

1 times m-reduction [i] would yield (13, 35, 9740)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 47928 826531 940206 918711 379601 085946 070473 464547 260223 > 32³⁵ [i]