MinT - Best Known (65−47, 65, s)-Nets in Base 32

Best Known (65−47, 65, s)-Nets in Base 32

(65−47, 65, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 65, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 65, 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]

(65−47, 65, 161)-Net over F₃₂ — Digital

Digital (18, 65, 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]

(65−47, 65, 177)-Net in Base 32 — Constructive

(18, 65, 177)-net in base 32, using

1 times m-reduction [i] based on (18, 66, 177)-net in base 32, using
- base change [i] based on digital (7, 55, 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]

(65−47, 65, 4680)-Net in Base 32 — Upper bound on s

There is no (18, 65, 4681)-net in base 32, because

1 times m-reduction [i] would yield (18, 64, 4681)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 145972 697854 426719 154047 818031 776822 508146 741431 222793 165551 966107 351001 240572 274321 704075 894944 > 32⁶⁴ [i]