MinT - Best Known (144−50, 144, s)-Nets in Base 5

Best Known (144−50, 144, s)-Nets in Base 5

(144−50, 144, 296)-Net over F₅ — Constructive and digital

Digital (94, 144, 296)-net over F₅, using

6 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(144−50, 144, 537)-Net over F₅ — Digital

Digital (94, 144, 537)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−50, 144, 26998)-Net in Base 5 — Upper bound on s

There is no (94, 144, 26999)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44862 230328 068429 219119 744282 254746 099329 796022 849876 822392 519812 805650 255799 471955 184848 081997 501821 > 5¹⁴⁴ [i]