MinT - Best Known (150−67, 150, s)-Nets in Base 5

Best Known (150−67, 150, s)-Nets in Base 5

(150−67, 150, 132)-Net over F₅ — Constructive and digital

Digital (83, 150, 132)-net over F₅, using

t-expansion [i] based on digital (79, 150, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 75, 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]

(150−67, 150, 214)-Net over F₅ — Digital

Digital (83, 150, 214)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−67, 150, 4688)-Net in Base 5 — Upper bound on s

There is no (83, 150, 4689)-net in base 5, because

1 times m-reduction [i] would yield (83, 149, 4689)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 842716 351623 770812 469468 595897 163949 098897 282913 113178 834253 471303 105211 292583 251840 280702 026287 240901 > 5¹⁴⁹ [i]