MinT - Best Known (18, 69, s)-Nets in Base 32

Best Known (18, 69, s)-Nets in Base 32

(18, 69, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 69, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 69, 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]

(18, 69, 128)-Net in Base 32 — Constructive

(18, 69, 128)-net in base 32, using

9 times m-reduction [i] based on (18, 78, 128)-net in base 32, using
- base change [i] based on digital (5, 65, 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]

(18, 69, 161)-Net over F₃₂ — Digital

Digital (18, 69, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(18, 69, 4063)-Net in Base 32 — Upper bound on s

There is no (18, 69, 4064)-net in base 32, because

1 times m-reduction [i] would yield (18, 68, 4064)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 245822 918439 996116 574411 591746 464538 948720 388130 629981 108690 958799 600701 503498 253411 617714 746172 676699 > 32⁶⁸ [i]