MinT - Best Known (15, 15+75, s)-Nets in Base 32

Best Known (15, 15+75, s)-Nets in Base 32

(15, 15+75, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 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]

(15, 15+75, 158)-Net over F₃₂ — Digital

Digital (15, 90, 158)-net over F₃₂, using

net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
  - an algebraic function field by Beelen and Pellikaan [i]

(15, 15+75, 1953)-Net in Base 32 — Upper bound on s

There is no (15, 90, 1954)-net in base 32, because

1 times m-reduction [i] would yield (15, 89, 1954)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 91 748294 357950 001322 051474 059626 324177 556715 385902 170083 205692 874022 951504 938497 002631 268388 353037 054200 536225 706581 996849 742165 787360 > 32⁸⁹ [i]