MinT - Best Known (124−43, 124, s)-Nets in Base 5

Best Known (124−43, 124, s)-Nets in Base 5

(124−43, 124, 296)-Net over F₅ — Constructive and digital

Digital (81, 124, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 62, 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]

(124−43, 124, 479)-Net over F₅ — Digital

Digital (81, 124, 479)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−43, 124, 26924)-Net in Base 5 — Upper bound on s

There is no (81, 124, 26925)-net in base 5, because

1 times m-reduction [i] would yield (81, 123, 26925)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 047857 097304 477145 010533 517484 413932 385451 590285 717245 395850 691807 520443 771638 785701 > 5¹²³ [i]