MinT - Best Known (102−81, 102, s)-Nets in Base 32

Best Known (102−81, 102, s)-Nets in Base 32

(102−81, 102, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 102, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 102, 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]

(102−81, 102, 185)-Net over F₃₂ — Digital

Digital (21, 102, 185)-net over F₃₂, using

net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
  - a curve from the manYPoints database [i]

(102−81, 102, 3192)-Net in Base 32 — Upper bound on s

There is no (21, 102, 3193)-net in base 32, because

1 times m-reduction [i] would yield (21, 101, 3193)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 105 528233 454601 416431 097646 124788 168102 540471 166884 061861 129824 252603 660891 582200 898238 821888 457559 129963 987287 388639 045818 365558 122537 169098 520148 365527 > 32¹⁰¹ [i]