MinT - Best Known (76, 76+38, s)-Nets in Base 5

Best Known (76, 76+38, s)-Nets in Base 5

(76, 76+38, 296)-Net over F₅ — Constructive and digital

Digital (76, 114, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 57, 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]

(76, 76+38, 535)-Net over F₅ — Digital

Digital (76, 114, 535)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+38, 30958)-Net in Base 5 — Upper bound on s

There is no (76, 114, 30959)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 157086 042630 666409 410255 508702 930367 594101 382498 581757 759029 951910 052040 708725 > 5¹¹⁴ [i]