MinT - Best Known (73−39, 73, s)-Nets in Base 32

Best Known (73−39, 73, s)-Nets in Base 32

(73−39, 73, 196)-Net over F₃₂ — Constructive and digital

Digital (34, 73, 196)-net over F₃₂, using

1 times m-reduction [i] based on digital (34, 74, 196)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 27, 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, 47, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(73−39, 73, 288)-Net in Base 32 — Constructive

(34, 73, 288)-net in base 32, using

t-expansion [i] based on (33, 73, 288)-net in base 32, using
- 11 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
  - base change [i] based on digital (9, 60, 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]

(73−39, 73, 386)-Net over F₃₂ — Digital

Digital (34, 73, 386)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−39, 73, 129284)-Net in Base 32 — Upper bound on s

There is no (34, 73, 129285)-net in base 32, because

1 times m-reduction [i] would yield (34, 72, 129285)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 348581 990360 985413 184954 560494 102173 737779 695823 463806 959160 061741 818701 781933 776965 545541 938807 719365 917760 > 32⁷² [i]