MinT - Best Known (68, 118, s)-Nets in Base 5

Best Known (68, 118, s)-Nets in Base 5

(68, 118, 208)-Net over F₅ — Constructive and digital

Digital (68, 118, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 59, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(68, 118, 213)-Net over F₅ — Digital

Digital (68, 118, 213)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 118, 5048)-Net in Base 5 — Upper bound on s

There is no (68, 118, 5049)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30207 295363 963311 961355 570840 320997 377121 825001 196461 915541 737249 305708 146952 294149 > 5¹¹⁸ [i]