MinT - Best Known (141−61, 141, s)-Nets in Base 5

Best Known (141−61, 141, s)-Nets in Base 5

(141−61, 141, 208)-Net over F₅ — Constructive and digital

Digital (80, 141, 208)-net over F₅, using

1 times m-reduction [i] based on digital (80, 142, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 71, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(141−61, 141, 228)-Net over F₅ — Digital

Digital (80, 141, 228)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−61, 141, 5480)-Net in Base 5 — Upper bound on s

There is no (80, 141, 5481)-net in base 5, because

1 times m-reduction [i] would yield (80, 140, 5481)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 787791 993188 176466 569589 632699 003081 142629 478604 452201 323368 718395 538570 941175 145763 676089 903529 > 5¹⁴⁰ [i]