MinT - Best Known (33, 33+59, s)-Nets in Base 32

Best Known (33, 33+59, s)-Nets in Base 32

(33, 33+59, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 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]

(33, 33+59, 216)-Net in Base 32 — Constructive

(33, 92, 216)-net in base 32, using

6 times m-reduction [i] based on (33, 98, 216)-net in base 32, using
- base change [i] based on digital (5, 70, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(33, 33+59, 273)-Net over F₃₂ — Digital

Digital (33, 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]

(33, 33+59, 19883)-Net in Base 32 — Upper bound on s

There is no (33, 92, 19884)-net in base 32, because

1 times m-reduction [i] would yield (33, 91, 19884)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93113 839011 150005 977219 504074 843000 901292 880940 492845 852856 454533 103015 817619 219441 228697 768156 752168 383730 947648 501768 008840 661910 362744 > 32⁹¹ [i]