MinT - Best Known (92−61, 92, s)-Nets in Base 32

Best Known (92−61, 92, s)-Nets in Base 32

(92−61, 92, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 92, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 92, 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]

(92−61, 92, 192)-Net in Base 32 — Constructive

(31, 92, 192)-net in base 32, using

6 times m-reduction [i] based on (31, 98, 192)-net in base 32, using
- base change [i] based on digital (3, 70, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(92−61, 92, 273)-Net over F₃₂ — Digital

Digital (31, 92, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 92, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(92−61, 92, 14275)-Net in Base 32 — Upper bound on s

There is no (31, 92, 14276)-net in base 32, because

1 times m-reduction [i] would yield (31, 91, 14276)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93216 421883 931384 342724 132843 884565 902798 631093 990970 815110 781832 742564 799264 839652 275112 263515 327073 171365 948602 292165 254361 616646 351216 > 32⁹¹ [i]