MinT - Best Known (78−58, 78, s)-Nets in Base 32

Best Known (78−58, 78, s)-Nets in Base 32

(78−58, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 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]

(78−58, 78, 177)-Net in Base 32 — Constructive

(20, 78, 177)-net in base 32, using

base change [i] based on digital (7, 65, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(78−58, 78, 177)-Net over F₃₂ — Digital

Digital (20, 78, 177)-net over F₃₂, using

net from sequence [i] based on digital (20, 176)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 20 and N(F) ≥ 177, using
  - a curve from the manYPoints database [i]

(78−58, 78, 4193)-Net in Base 32 — Upper bound on s

There is no (20, 78, 4194)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2534 612791 878513 803513 231100 915941 566675 718414 006558 750901 115223 137980 479621 839325 957903 824786 102983 626302 199345 754328 > 32⁷⁸ [i]