MinT - Best Known (87−67, 87, s)-Nets in Base 32

Best Known (87−67, 87, s)-Nets in Base 32

(87−67, 87, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 87, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 87, 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]

(87−67, 87, 128)-Net in Base 32 — Constructive

(20, 87, 128)-net in base 32, using

3 times m-reduction [i] based on (20, 90, 128)-net in base 32, using
- base change [i] based on digital (5, 75, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(87−67, 87, 177)-Net over F₃₂ — Digital

Digital (20, 87, 177)-net over F₃₂, using

net from sequence [i] based on digital (20, 176)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 20 and N(F) ≥ 177, using
  - a curve from the manYPoints database [i]

(87−67, 87, 3535)-Net in Base 32 — Upper bound on s

There is no (20, 87, 3536)-net in base 32, because

1 times m-reduction [i] would yield (20, 86, 3536)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2793 064271 099494 724696 493332 597803 455711 441575 959021 535622 417566 116354 265347 914839 225099 208546 468226 994609 993636 031369 990631 597506 > 32⁸⁶ [i]