MinT - Best Known (25, 108, s)-Nets in Base 32

Best Known (25, 108, s)-Nets in Base 32

(25, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(25, 108, 177)-Net in Base 32 — Constructive

(25, 108, 177)-net in base 32, using

base change [i] based on digital (7, 90, 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]

(25, 108, 225)-Net over F₃₂ — Digital

Digital (25, 108, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 108, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(25, 108, 4390)-Net in Base 32 — Upper bound on s

There is no (25, 108, 4391)-net in base 32, because

1 times m-reduction [i] would yield (25, 107, 4391)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112893 539897 843233 650861 689134 470640 329128 096085 897052 109191 963640 826214 895618 964705 485034 627151 748448 348589 352797 023982 637829 658353 624623 435110 392371 863355 564352 > 32¹⁰⁷ [i]