MinT - Best Known (98−77, 98, s)-Nets in Base 32

Best Known (98−77, 98, s)-Nets in Base 32

(98−77, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 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]

(98−77, 98, 185)-Net over F₃₂ — Digital

Digital (21, 98, 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]

(98−77, 98, 3349)-Net in Base 32 — Upper bound on s

There is no (21, 98, 3350)-net in base 32, because

1 times m-reduction [i] would yield (21, 97, 3350)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 100 391292 259359 226665 397828 623440 030141 692385 161247 208355 463828 855674 873833 442286 710033 978578 853530 578716 054302 209293 418917 594403 618671 241593 189440 > 32⁹⁷ [i]