MinT - Best Known (146−51, 146, s)-Nets in Base 5

Best Known (146−51, 146, s)-Nets in Base 5

(146−51, 146, 296)-Net over F₅ — Constructive and digital

Digital (95, 146, 296)-net over F₅, using

t-expansion [i] based on digital (94, 146, 296)-net over F₅, using
- 4 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]

(146−51, 146, 529)-Net over F₅ — Digital

Digital (95, 146, 529)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−51, 146, 28794)-Net in Base 5 — Upper bound on s

There is no (95, 146, 28795)-net in base 5, because

1 times m-reduction [i] would yield (95, 145, 28795)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224211 933872 425905 440956 755348 957539 657606 032198 641485 341695 044917 867487 440298 188245 650507 855352 950669 > 5¹⁴⁵ [i]