MinT - Best Known (80−44, 80, s)-Nets in Base 32

Best Known (80−44, 80, s)-Nets in Base 32

(80−44, 80, 196)-Net over F₃₂ — Constructive and digital

Digital (36, 80, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 29, 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 (7, 51, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(80−44, 80, 288)-Net in Base 32 — Constructive

(36, 80, 288)-net in base 32, using

t-expansion [i] based on (35, 80, 288)-net in base 32, using
- 11 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
  - base change [i] based on digital (9, 65, 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]

(80−44, 80, 344)-Net over F₃₂ — Digital

Digital (36, 80, 344)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−44, 80, 86837)-Net in Base 32 — Upper bound on s

There is no (36, 80, 86838)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 582496 806398 851082 747207 677362 954203 213267 234837 780836 748044 904882 039189 092009 429515 334932 417388 327847 106465 260910 016912 > 32⁸⁰ [i]