MinT - Best Known (51−43, 51, s)-Nets in Base 32

Best Known (51−43, 51, s)-Nets in Base 32

(51−43, 51, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 51, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 51, 98)-net over F₃₂, using
- net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
    - a function field by SÃ©mirat [i]

(51−43, 51, 1062)-Net in Base 32 — Upper bound on s

There is no (8, 51, 1063)-net in base 32, because

1 times m-reduction [i] would yield (8, 50, 1063)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1813 016849 724985 867494 666791 267552 523946 047688 451938 003919 999227 054414 734316 > 32⁵⁰ [i]