MinT - Best Known (60−47, 60, s)-Nets in Base 32

Best Known (60−47, 60, s)-Nets in Base 32

(60−47, 60, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 60, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 60, 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]

(60−47, 60, 129)-Net over F₃₂ — Digital

Digital (13, 60, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 60, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(60−47, 60, 2196)-Net in Base 32 — Upper bound on s

There is no (13, 60, 2197)-net in base 32, because

1 times m-reduction [i] would yield (13, 59, 2197)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 63693 741373 262447 278290 717681 300566 025750 317671 016655 067042 727571 985390 695544 010132 579200 > 32⁵⁹ [i]