MinT - Best Known (117−38, 117, s)-Nets in Base 5

Best Known (117−38, 117, s)-Nets in Base 5

(117−38, 117, 296)-Net over F₅ — Constructive and digital

Digital (79, 117, 296)-net over F₅, using

3 times m-reduction [i] based on digital (79, 120, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 60, 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]

(117−38, 117, 613)-Net over F₅ — Digital

Digital (79, 117, 613)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−38, 117, 39919)-Net in Base 5 — Upper bound on s

There is no (79, 117, 39920)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6018 754933 536161 935622 533943 267474 805428 716315 565508 348740 151223 249964 330118 738369 > 5¹¹⁷ [i]