MinT - Best Known (19, 19+79, s)-Nets in Base 32

Best Known (19, 19+79, s)-Nets in Base 32

(19, 19+79, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(19, 19+79, 172)-Net over F₃₂ — Digital

Digital (19, 98, 172)-net over F₃₂, using

net from sequence [i] based on digital (19, 171)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 19 and N(F) ≥ 172, using
  - a curve from the manYPoints database [i]

(19, 19+79, 2731)-Net in Base 32 — Upper bound on s

There is no (19, 98, 2732)-net in base 32, because

1 times m-reduction [i] would yield (19, 97, 2732)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 100 277020 378566 828726 290604 443540 476834 014852 460289 352966 447378 910709 171015 308726 353809 023671 442465 159539 706204 495384 419259 461812 014125 318762 322134 > 32⁹⁷ [i]