MinT - Best Known (51−38, 51, s)-Nets in Base 32

Best Known (51−38, 51, s)-Nets in Base 32

(51−38, 51, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 51, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 51, 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]

(51−38, 51, 129)-Net over F₃₂ — Digital

Digital (13, 51, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 51, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(51−38, 51, 2795)-Net in Base 32 — Upper bound on s

There is no (13, 51, 2796)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 57980 657414 828909 567680 944162 767610 018270 388728 455442 350520 441270 734482 021226 > 32⁵¹ [i]