MinT - Best Known (13, 48, s)-Nets in Base 32

Best Known (13, 48, s)-Nets in Base 32

(13, 48, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 48, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 48, 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, 48, 128)-Net in Base 32 — Constructive

(13, 48, 128)-net in base 32, using

base change [i] based on digital (5, 40, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(13, 48, 129)-Net over F₃₂ — Digital

Digital (13, 48, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 48, 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, 48, 133)-Net in Base 32

(13, 48, 133)-net in base 32, using

base change [i] based on digital (5, 40, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(13, 48, 3347)-Net in Base 32 — Upper bound on s

There is no (13, 48, 3348)-net in base 32, because

1 times m-reduction [i] would yield (13, 47, 3348)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 55239 401101 045409 315266 151530 809400 561573 580617 506026 770241 614949 712133 > 32⁴⁷ [i]