MinT - Best Known (21, 21+37, s)-Nets in Base 32

Best Known (21, 21+37, s)-Nets in Base 32

(21, 21+37, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 58, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 58, 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]

(21, 21+37, 185)-Net over F₃₂ — Digital

Digital (21, 58, 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]

(21, 21+37, 192)-Net in Base 32 — Constructive

(21, 58, 192)-net in base 32, using

5 times m-reduction [i] based on (21, 63, 192)-net in base 32, using
- base change [i] based on digital (3, 45, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(21, 21+37, 225)-Net in Base 32

(21, 58, 225)-net in base 32, using

8 times m-reduction [i] based on (21, 66, 225)-net in base 32, using
- base change [i] based on digital (10, 55, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(21, 21+37, 14216)-Net in Base 32 — Upper bound on s

There is no (21, 58, 14217)-net in base 32, because

1 times m-reduction [i] would yield (21, 57, 14217)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 62 187564 100293 032951 553589 625282 826783 465287 125493 724897 930560 424517 298519 149464 414560 > 32⁵⁷ [i]