MinT - Best Known (90−82, 90, s)-Nets in Base 32

Best Known (90−82, 90, s)-Nets in Base 32

(90−82, 90, 98)-Net over F₃₂ — Constructive and digital

Digital (8, 90, 98)-net over F₃₂, using

t-expansion [i] based on digital (7, 90, 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]

(90−82, 90, 987)-Net in Base 32 — Upper bound on s

There is no (8, 90, 988)-net in base 32, because

20 times m-reduction [i] would yield (8, 70, 988)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2345 291437 460818 500110 765504 625663 782701 764341 298880 831201 653989 145348 590083 314433 572625 094379 654654 249136 > 32⁷⁰ [i]