MinT - Best Known (19, 19+45, s)-Nets in Base 32

Best Known (19, 19+45, s)-Nets in Base 32

(19, 19+45, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 64, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 64, 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+45, 172)-Net over F₃₂ — Digital

Digital (19, 64, 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+45, 177)-Net in Base 32 — Constructive

(19, 64, 177)-net in base 32, using

8 times m-reduction [i] based on (19, 72, 177)-net in base 32, using
- base change [i] based on digital (7, 60, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(19, 19+45, 5954)-Net in Base 32 — Upper bound on s

There is no (19, 64, 5955)-net in base 32, because

1 times m-reduction [i] would yield (19, 63, 5955)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 66765 249516 643788 700539 819184 208501 031588 605393 385092 617143 756211 209135 572228 035222 735698 259536 > 32⁶³ [i]