MinT - Best Known (38, 38+30, s)-Nets in Base 5

Best Known (38, 38+30, s)-Nets in Base 5

(38, 38+30, 132)-Net over F₅ — Constructive and digital

Digital (38, 68, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 34, 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]

(38, 38+30, 2357)-Net in Base 5 — Upper bound on s

There is no (38, 68, 2358)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 340517 816727 601822 684679 363415 435152 597219 645945 > 5⁶⁸ [i]