MinT - Best Known (144−67, 144, s)-Nets in Base 5

Best Known (144−67, 144, s)-Nets in Base 5

(144−67, 144, 132)-Net over F₅ — Constructive and digital

Digital (77, 144, 132)-net over F₅, using

2 times m-reduction [i] based on digital (77, 146, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 73, 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]

(144−67, 144, 180)-Net over F₅ — Digital

Digital (77, 144, 180)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−67, 144, 3492)-Net in Base 5 — Upper bound on s

There is no (77, 144, 3493)-net in base 5, because

1 times m-reduction [i] would yield (77, 143, 3493)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8989 966081 768547 161630 400021 335596 294249 846616 597455 507451 170504 745014 143154 544886 534954 322825 196565 > 5¹⁴³ [i]