MinT - Best Known (99−44, 99, s)-Nets in Base 5

Best Known (99−44, 99, s)-Nets in Base 5

(99−44, 99, 132)-Net over F₅ — Constructive and digital

Digital (55, 99, 132)-net over F₅, using

3 times m-reduction [i] based on digital (55, 102, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 51, 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]

(99−44, 99, 156)-Net over F₅ — Digital

Digital (55, 99, 156)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−44, 99, 3147)-Net in Base 5 — Upper bound on s

There is no (55, 99, 3148)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1583 681249 270419 449330 056518 698637 670654 214726 563023 118454 509799 885121 > 5⁹⁹ [i]