MinT - Best Known (19, 19+28, s)-Nets in Base 32

Best Known (19, 19+28, s)-Nets in Base 32

(19, 19+28, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 47, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 47, 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+28, 172)-Net over F₃₂ — Digital

Digital (19, 47, 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+28, 258)-Net in Base 32 — Constructive

(19, 47, 258)-net in base 32, using

1 times m-reduction [i] based on (19, 48, 258)-net in base 32, using
- base change [i] based on digital (1, 30, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(19, 19+28, 289)-Net in Base 32

(19, 47, 289)-net in base 32, using

1 times m-reduction [i] based on (19, 48, 289)-net in base 32, using
- base change [i] based on digital (1, 30, 289)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(19, 19+28, 22027)-Net in Base 32 — Upper bound on s

There is no (19, 47, 22028)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 55236 307453 387135 933649 606854 944767 313883 241813 105685 388172 875390 836096 > 32⁴⁷ [i]