MinT - Best Known (84−43, 84, s)-Nets in Base 32

Best Known (84−43, 84, s)-Nets in Base 32

(84−43, 84, 224)-Net over F₃₂ — Constructive and digital

Digital (41, 84, 224)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 30, 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]
2. digital (11, 54, 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]

(84−43, 84, 288)-Net in Base 32 — Constructive

(41, 84, 288)-net in base 32, using

t-expansion [i] based on (40, 84, 288)-net in base 32, using
- 24 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 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]

(84−43, 84, 562)-Net over F₃₂ — Digital

Digital (41, 84, 562)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−43, 84, 248907)-Net in Base 32 — Upper bound on s

There is no (41, 84, 248908)-net in base 32, because

1 times m-reduction [i] would yield (41, 83, 248908)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 84617 236087 124230 926841 220265 665721 295688 966080 638472 354307 916867 622392 997959 921720 855863 947788 376900 428907 177709 355435 347832 > 32⁸³ [i]