MinT - Best Known (90−73, 90, s)-Nets in Base 32

Best Known (90−73, 90, s)-Nets in Base 32

(90−73, 90, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 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]

(90−73, 90, 158)-Net over F₃₂ — Digital

Digital (17, 90, 158)-net over F₃₂, using

t-expansion [i] based on 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]

(90−73, 90, 2404)-Net in Base 32 — Upper bound on s

There is no (17, 90, 2405)-net in base 32, because

1 times m-reduction [i] would yield (17, 89, 2405)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 91 049173 008841 598379 118091 051007 143508 464864 346892 534845 495266 483169 317895 989416 474337 888052 207042 377936 371341 858954 755197 295735 405207 > 32⁸⁹ [i]