MinT - Best Known (52, 88, s)-Nets in Base 32

Best Known (52, 88, s)-Nets in Base 32

(52, 88, 294)-Net over F₃₂ — Constructive and digital

Digital (52, 88, 294)-net over F₃₂, using

2 times m-reduction [i] based on digital (52, 90, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 19, 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, 26, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 45, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(52, 88, 515)-Net in Base 32 — Constructive

(52, 88, 515)-net in base 32, using

base change [i] based on digital (19, 55, 515)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 18, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 37, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(52, 88, 2748)-Net over F₃₂ — Digital

Digital (52, 88, 2748)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 88, 5562610)-Net in Base 32 — Upper bound on s

There is no (52, 88, 5562611)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 839217 446144 670620 655786 177412 778877 500679 467881 388872 891586 689618 560441 987963 023284 149940 556250 612466 685264 903540 211092 264657 665539 > 32⁸⁸ [i]