MinT - Best Known (73−49, 73, s)-Nets in Base 32

Best Known (73−49, 73, s)-Nets in Base 32

(73−49, 73, 120)-Net over F₃₂ — Constructive and digital

Digital (24, 73, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 73, 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]

(73−49, 73, 177)-Net in Base 32 — Constructive

(24, 73, 177)-net in base 32, using

29 times m-reduction [i] based on (24, 102, 177)-net in base 32, using
- base change [i] based on digital (7, 85, 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]

(73−49, 73, 225)-Net over F₃₂ — Digital

Digital (24, 73, 225)-net over F₃₂, using

net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(73−49, 73, 10349)-Net in Base 32 — Upper bound on s

There is no (24, 73, 10350)-net in base 32, because

1 times m-reduction [i] would yield (24, 72, 10350)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 349057 683432 225298 766389 195339 317082 132254 241119 921052 694707 948179 429222 651857 384833 795844 849940 178221 022706 > 32⁷² [i]