MinT - Best Known (48, 80, s)-Nets in Base 32

Best Known (48, 80, s)-Nets in Base 32

(48, 80, 294)-Net over F₃₂ — Constructive and digital

Digital (48, 80, 294)-net over F₃₂, using

1 times m-reduction [i] based on digital (48, 81, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 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, 23, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 40, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(48, 80, 516)-Net in Base 32 — Constructive

(48, 80, 516)-net in base 32, using

base change [i] based on digital (18, 50, 516)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 17, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
  2. digital (1, 33, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(48, 80, 3084)-Net over F₃₂ — Digital

Digital (48, 80, 3084)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 80, 7360824)-Net in Base 32 — Upper bound on s

There is no (48, 80, 7360825)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 582253 997129 278605 162378 491791 031714 092585 665241 048957 371765 804931 419877 281637 904512 134730 052962 020047 951652 238694 433561 > 32⁸⁰ [i]