MinT - Best Known (146−64, 146, s)-Nets in Base 5

Best Known (146−64, 146, s)-Nets in Base 5

(146−64, 146, 208)-Net over F₅ — Constructive and digital

Digital (82, 146, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 73, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(146−64, 146, 224)-Net over F₅ — Digital

Digital (82, 146, 224)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−64, 146, 4918)-Net in Base 5 — Upper bound on s

There is no (82, 146, 4919)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 127014 505837 787157 725230 693358 432596 033889 377593 904745 862837 485574 582819 681719 971289 713264 515011 659649 > 5¹⁴⁶ [i]