MinT - Best Known (89−59, 89, s)-Nets in Base 32

Best Known (89−59, 89, s)-Nets in Base 32

(89−59, 89, 120)-Net over F₃₂ — Constructive and digital

Digital (30, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(89−59, 89, 192)-Net in Base 32 — Constructive

(30, 89, 192)-net in base 32, using

t-expansion [i] based on (29, 89, 192)-net in base 32, using
- 2 times m-reduction [i] based on (29, 91, 192)-net in base 32, using
  - base change [i] based on digital (3, 65, 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]

(89−59, 89, 273)-Net over F₃₂ — Digital

Digital (30, 89, 273)-net over F₃₂, using

net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
  - a curve from the manYPoints database [i]

(89−59, 89, 13888)-Net in Base 32 — Upper bound on s

There is no (30, 89, 13889)-net in base 32, because

1 times m-reduction [i] would yield (30, 88, 13889)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 844079 385092 334289 672021 266763 385950 208714 050512 834610 496382 864206 918471 950914 586420 057006 849327 168449 753983 681179 951245 009672 025024 > 32⁸⁸ [i]