MinT - Best Known (92−77, 92, s)-Nets in Base 32

Best Known (92−77, 92, s)-Nets in Base 32

(92−77, 92, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 92, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 92, 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]

(92−77, 92, 158)-Net over F₃₂ — Digital

Digital (15, 92, 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]

(92−77, 92, 1929)-Net in Base 32 — Upper bound on s

There is no (15, 92, 1930)-net in base 32, because

1 times m-reduction [i] would yield (15, 91, 1930)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93725 208975 865285 733265 594069 876527 312283 982283 374890 344865 568033 956910 071371 470467 660439 484839 150818 308267 398538 540661 744986 620642 172496 > 32⁹¹ [i]