MinT - Best Known (144−65, 144, s)-Nets in Base 5

Best Known (144−65, 144, s)-Nets in Base 5

(144−65, 144, 132)-Net over F₅ — Constructive and digital

Digital (79, 144, 132)-net over F₅, using

6 times m-reduction [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]

(144−65, 144, 200)-Net over F₅ — Digital

Digital (79, 144, 200)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−65, 144, 4226)-Net in Base 5 — Upper bound on s

There is no (79, 144, 4227)-net in base 5, because

1 times m-reduction [i] would yield (79, 143, 4227)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9029 777094 311432 317597 254420 759000 186220 464974 084107 035018 666053 993289 672737 265127 881944 114170 442625 > 5¹⁴³ [i]