MinT - Best Known (87−50, 87, s)-Nets in Base 32

Best Known (87−50, 87, s)-Nets in Base 32

(87−50, 87, 174)-Net over F₃₂ — Constructive and digital

Digital (37, 87, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 30, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 57, 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]

(87−50, 87, 282)-Net over F₃₂ — Digital

Digital (37, 87, 282)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−50, 87, 288)-Net in Base 32 — Constructive

(37, 87, 288)-net in base 32, using

11 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]

(87−50, 87, 342)-Net in Base 32

(37, 87, 342)-net in base 32, using

15 times m-reduction [i] based on (37, 102, 342)-net in base 32, using
- base change [i] based on digital (20, 85, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(87−50, 87, 56765)-Net in Base 32 — Upper bound on s

There is no (37, 87, 56766)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 88726 432567 131930 303240 755466 052674 163407 869894 989492 095067 075394 583966 762365 828461 239273 066570 593783 173347 211551 070843 906540 902347 > 32⁸⁷ [i]