MinT - Best Known (88−57, 88, s)-Nets in Base 32

Best Known (88−57, 88, s)-Nets in Base 32

(88−57, 88, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 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]

(88−57, 88, 216)-Net in Base 32 — Constructive

(31, 88, 216)-net in base 32, using

3 times m-reduction [i] based on (31, 91, 216)-net in base 32, using
- base change [i] based on digital (5, 65, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(88−57, 88, 273)-Net over F₃₂ — Digital

Digital (31, 88, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 88, 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]

(88−57, 88, 17298)-Net in Base 32 — Upper bound on s

There is no (31, 88, 17299)-net in base 32, because

1 times m-reduction [i] would yield (31, 87, 17299)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 88857 317253 167246 736902 019671 455061 493567 673215 009058 016886 482475 634286 275249 497751 594997 985941 837174 962745 221737 137668 333729 880544 > 32⁸⁷ [i]