MinT - Best Known (35, 80, s)-Nets in Base 32

Best Known (35, 80, s)-Nets in Base 32

(35, 80, 174)-Net over F₃₂ — Constructive and digital

Digital (35, 80, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (35, 81, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 28, 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, 53, 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]

(35, 80, 288)-Net in Base 32 — Constructive

(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]

(35, 80, 300)-Net over F₃₂ — Digital

Digital (35, 80, 300)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(35, 80, 342)-Net in Base 32

(35, 80, 342)-net in base 32, using

10 times m-reduction [i] based on (35, 90, 342)-net in base 32, using
- base change [i] based on digital (20, 75, 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]

(35, 80, 74179)-Net in Base 32 — Upper bound on s

There is no (35, 80, 74180)-net in base 32, because

1 times m-reduction [i] would yield (35, 79, 74180)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80713 201340 342582 837762 056092 381196 467418 014082 408265 321330 485889 759317 209561 298354 756334 835115 620030 590130 142869 503376 > 32⁷⁹ [i]