MinT - Best Known (101−87, 101, s)-Nets in Base 32

Best Known (101−87, 101, s)-Nets in Base 32

(101−87, 101, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 101, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 101, 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]

(101−87, 101, 146)-Net over F₃₂ — Digital

Digital (14, 101, 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]

(101−87, 101, 1701)-Net in Base 32 — Upper bound on s

There is no (14, 101, 1702)-net in base 32, because

1 times m-reduction [i] would yield (14, 100, 1702)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 326826 448787 098225 880286 242620 195250 478471 405310 660219 438890 211733 560466 149895 357849 822973 443633 852427 119530 218274 351945 346611 016474 852941 133908 858400 > 32¹⁰⁰ [i]