MinT - Best Known (19, 19+30, s)-Nets in Base 32

Best Known (19, 19+30, s)-Nets in Base 32

(19, 19+30, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 49, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 49, 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+30, 172)-Net over F₃₂ — Digital

Digital (19, 49, 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+30, 257)-Net in Base 32 — Constructive

(19, 49, 257)-net in base 32, using

32¹ times duplication [i] based on (18, 48, 257)-net in base 32, using
- base change [i] based on digital (0, 30, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(19, 19+30, 17101)-Net in Base 32 — Upper bound on s

There is no (19, 49, 17102)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 56 556059 332346 055315 230653 840657 705024 593932 663232 296840 787094 588323 908448 > 32⁴⁹ [i]