MinT - Best Known (146−54, 146, s)-Nets in Base 5

Best Known (146−54, 146, s)-Nets in Base 5

(146−54, 146, 296)-Net over F₅ — Constructive and digital

Digital (92, 146, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 73, 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]

(146−54, 146, 420)-Net over F₅ — Digital

Digital (92, 146, 420)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−54, 146, 16422)-Net in Base 5 — Upper bound on s

There is no (92, 146, 16423)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 121866 438278 362156 715109 593207 699622 667638 497062 742230 070198 139401 949354 145068 588177 034231 784139 634869 > 5¹⁴⁶ [i]