MinT - Best Known (16, 16+77, s)-Nets in Base 32

Best Known (16, 16+77, s)-Nets in Base 32

(16, 16+77, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 93, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 93, 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]

(16, 16+77, 158)-Net over F₃₂ — Digital

Digital (16, 93, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 93, 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]

(16, 16+77, 2115)-Net in Base 32 — Upper bound on s

There is no (16, 93, 2116)-net in base 32, because

1 times m-reduction [i] would yield (16, 92, 2116)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 989860 888378 243026 354943 145989 150201 822005 988419 563098 814440 805867 098601 582563 538487 304482 107344 372526 398968 350559 801422 579155 037221 014352 > 32⁹² [i]