MinT - Best Known (90, 90+52, s)-Nets in Base 5

Best Known (90, 90+52, s)-Nets in Base 5

(90, 90+52, 296)-Net over F₅ — Constructive and digital

Digital (90, 142, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 71, 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]

(90, 90+52, 427)-Net over F₅ — Digital

Digital (90, 142, 427)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+52, 17306)-Net in Base 5 — Upper bound on s

There is no (90, 142, 17307)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1795 113585 964174 780321 276403 066743 540717 005587 131348 490101 687288 890370 530362 971612 109472 126167 016217 > 5¹⁴² [i]