MinT - Best Known (37, 80, s)-Nets in Base 32

Best Known (37, 80, s)-Nets in Base 32

(37, 80, 202)-Net over F₃₂ — Constructive and digital

Digital (37, 80, 202)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 28, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (9, 52, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(37, 80, 288)-Net in Base 32 — Constructive

(37, 80, 288)-net in base 32, using

18 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(37, 80, 397)-Net over F₃₂ — Digital

Digital (37, 80, 397)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 80, 128625)-Net in Base 32 — Upper bound on s

There is no (37, 80, 128626)-net in base 32, because

1 times m-reduction [i] would yield (37, 79, 128626)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80707 285502 199324 713311 070524 914116 038780 735475 551428 364333 401975 009793 703475 589367 544173 098132 434425 713151 150267 287432 > 32⁷⁹ [i]