MinT - Best Known (150−54, 150, s)-Nets in Base 5

Best Known (150−54, 150, s)-Nets in Base 5

(150−54, 150, 296)-Net over F₅ — Constructive and digital

Digital (96, 150, 296)-net over F₅, using

t-expansion [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]

(150−54, 150, 478)-Net over F₅ — Digital

Digital (96, 150, 478)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−54, 150, 20849)-Net in Base 5 — Upper bound on s

There is no (96, 150, 20850)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 700 807702 858493 166660 809848 636922 331030 659813 967672 306245 870436 055023 834649 083473 485588 680984 637006 240617 > 5¹⁵⁰ [i]