MinT - Best Known (142−41, 142, s)-Nets in Base 5

Best Known (142−41, 142, s)-Nets in Base 5

(142−41, 142, 408)-Net over F₅ — Constructive and digital

Digital (101, 142, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 71, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(142−41, 142, 1214)-Net over F₅ — Digital

Digital (101, 142, 1214)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−41, 142, 175771)-Net in Base 5 — Upper bound on s

There is no (101, 142, 175772)-net in base 5, because

1 times m-reduction [i] would yield (101, 141, 175772)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 358 744764 967528 862253 166752 733937 941103 998845 668932 582746 207534 770717 717597 746477 776320 467447 217921 > 5¹⁴¹ [i]