MinT - Best Known (143−65, 143, s)-Nets in Base 5

Best Known (143−65, 143, s)-Nets in Base 5

(143−65, 143, 132)-Net over F₅ — Constructive and digital

Digital (78, 143, 132)-net over F₅, using

5 times m-reduction [i] based on digital (78, 148, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 74, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(143−65, 143, 194)-Net over F₅ — Digital

Digital (78, 143, 194)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−65, 143, 4017)-Net in Base 5 — Upper bound on s

There is no (78, 143, 4018)-net in base 5, because

1 times m-reduction [i] would yield (78, 142, 4018)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1798 634716 937185 552389 915957 291396 114758 172017 839306 459843 773417 955128 219652 526295 603961 758959 343105 > 5¹⁴² [i]