MinT - Best Known (147−52, 147, s)-Nets in Base 5

Best Known (147−52, 147, s)-Nets in Base 5

(147−52, 147, 296)-Net over F₅ — Constructive and digital

Digital (95, 147, 296)-net over F₅, using

t-expansion [i] based on digital (94, 147, 296)-net over F₅, using
- 3 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]

(147−52, 147, 505)-Net over F₅ — Digital

Digital (95, 147, 505)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−52, 147, 23591)-Net in Base 5 — Upper bound on s

There is no (95, 147, 23592)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 609343 467591 896273 940018 281842 946767 344809 856522 187784 321189 702849 459318 699747 378596 949355 436461 292673 > 5¹⁴⁷ [i]