MinT - Best Known (105−85, 105, s)-Nets in Base 32

Best Known (105−85, 105, s)-Nets in Base 32

(105−85, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 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]

(105−85, 105, 177)-Net over F₃₂ — Digital

Digital (20, 105, 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]

(105−85, 105, 2819)-Net in Base 32 — Upper bound on s

There is no (20, 105, 2820)-net in base 32, because

1 times m-reduction [i] would yield (20, 104, 2820)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 471858 214838 627336 383590 974984 589680 500761 864950 757085 732810 385033 731694 981513 033769 755854 349617 933425 308002 174646 105965 141077 409662 654105 054346 052679 371232 > 32¹⁰⁴ [i]