MinT - Best Known (90−71, 90, s)-Nets in Base 32

Best Known (90−71, 90, s)-Nets in Base 32

(90−71, 90, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 90, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 90, 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]

(90−71, 90, 172)-Net over F₃₂ — Digital

Digital (19, 90, 172)-net over F₃₂, using

net from sequence [i] based on digital (19, 171)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 19 and N(F) ≥ 172, using
  - a curve from the manYPoints database [i]

(90−71, 90, 2996)-Net in Base 32 — Upper bound on s

There is no (19, 90, 2997)-net in base 32, because

1 times m-reduction [i] would yield (19, 89, 2997)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 90 994459 395207 992626 343086 833751 625566 662198 454396 392020 066095 596501 176784 697377 180324 486064 361954 960712 712306 067945 926812 393752 998756 > 32⁸⁹ [i]