MinT - Best Known (91−74, 91, s)-Nets in Base 32

Best Known (91−74, 91, s)-Nets in Base 32

(91−74, 91, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 91, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 91, 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]

(91−74, 91, 158)-Net over F₃₂ — Digital

Digital (17, 91, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 91, 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]

(91−74, 91, 2359)-Net in Base 32 — Upper bound on s

There is no (17, 91, 2360)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93180 058108 104087 288931 160826 469945 166600 708535 980945 866878 196187 249947 107105 050367 469397 340334 049514 930378 848624 474015 362526 272920 468393 > 32⁹¹ [i]