MinT - Best Known (65−51, 65, s)-Nets in Base 32

Best Known (65−51, 65, s)-Nets in Base 32

(65−51, 65, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 65, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 65, 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]

(65−51, 65, 146)-Net over F₃₂ — Digital

Digital (14, 65, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(65−51, 65, 2328)-Net in Base 32 — Upper bound on s

There is no (14, 65, 2329)-net in base 32, because

1 times m-reduction [i] would yield (14, 64, 2329)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 148327 243722 314179 895144 319828 882837 927113 082992 309319 904583 114321 974990 823295 701335 234285 370400 > 32⁶⁴ [i]