MinT - Best Known (78, 78+40, s)-Nets in Base 5

Best Known (78, 78+40, s)-Nets in Base 5

(78, 78+40, 296)-Net over F₅ — Constructive and digital

Digital (78, 118, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 59, 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]

(78, 78+40, 509)-Net over F₅ — Digital

Digital (78, 118, 509)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+40, 27602)-Net in Base 5 — Upper bound on s

There is no (78, 118, 27603)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30113 525160 471768 815645 167248 636658 084054 722604 420904 694412 275324 307385 059049 008945 > 5¹¹⁸ [i]