MinT - Best Known (37−23, 37, s)-Nets in Base 32

Best Known (37−23, 37, s)-Nets in Base 32

(37−23, 37, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 37, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 37, 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]

(37−23, 37, 146)-Net over F₃₂ — Digital

Digital (14, 37, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(37−23, 37, 177)-Net in Base 32 — Constructive

(14, 37, 177)-net in base 32, using

5 times m-reduction [i] based on (14, 42, 177)-net in base 32, using
- base change [i] based on digital (7, 35, 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]

(37−23, 37, 13348)-Net in Base 32 — Upper bound on s

There is no (14, 37, 13349)-net in base 32, because

1 times m-reduction [i] would yield (14, 36, 13349)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 533468 148730 293088 968289 503938 189316 581436 099392 090960 > 32³⁶ [i]