MinT - Best Known (134−42, 134, s)-Nets in Base 5

Best Known (134−42, 134, s)-Nets in Base 5

(134−42, 134, 400)-Net over F₅ — Constructive and digital

Digital (92, 134, 400)-net over F₅, using

trace code for nets [i] based on digital (25, 67, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(134−42, 134, 797)-Net over F₅ — Digital

Digital (92, 134, 797)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−42, 134, 62577)-Net in Base 5 — Upper bound on s

There is no (92, 134, 62578)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4591 908745 835092 054411 194282 953231 904070 686227 480357 139752 905522 960176 073256 411860 674321 580745 > 5¹³⁴ [i]