MinT - Best Known (73−56, 73, s)-Nets in Base 32

Best Known (73−56, 73, s)-Nets in Base 32

(73−56, 73, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 73, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 73, 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]

(73−56, 73, 158)-Net over F₃₂ — Digital

Digital (17, 73, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 73, 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]

(73−56, 73, 3046)-Net in Base 32 — Upper bound on s

There is no (17, 73, 3047)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 75 805896 028493 317608 376208 767797 585288 797921 789111 389808 314432 344080 489725 045800 325025 957428 917999 591846 089940 > 32⁷³ [i]