MinT - Best Known (126−44, 126, s)-Nets in Base 5

Best Known (126−44, 126, s)-Nets in Base 5

(126−44, 126, 296)-Net over F₅ — Constructive and digital

Digital (82, 126, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 63, 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]

(126−44, 126, 471)-Net over F₅ — Digital

Digital (82, 126, 471)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−44, 126, 22786)-Net in Base 5 — Upper bound on s

There is no (82, 126, 22787)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11759 131328 360310 330612 868412 971411 515827 922997 422649 834408 691589 436525 100288 300425 197225 > 5¹²⁶ [i]