MinT - Best Known (30, 30+61, s)-Nets in Base 32

Best Known (30, 30+61, s)-Nets in Base 32

(30, 30+61, 120)-Net over F₃₂ — Constructive and digital

Digital (30, 91, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 91, 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]

(30, 30+61, 192)-Net in Base 32 — Constructive

(30, 91, 192)-net in base 32, using

t-expansion [i] based on (29, 91, 192)-net in base 32, using
- base change [i] based on digital (3, 65, 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]

(30, 30+61, 273)-Net over F₃₂ — Digital

Digital (30, 91, 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]

(30, 30+61, 12715)-Net in Base 32 — Upper bound on s

There is no (30, 91, 12716)-net in base 32, because

1 times m-reduction [i] would yield (30, 90, 12716)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2907 641010 812791 902718 316905 428002 726266 880423 086811 589648 530420 515207 489744 549668 323148 854099 058997 506990 312864 686170 330544 789368 379080 > 32⁹⁰ [i]