MinT - Best Known (118−55, 118, s)-Nets in Base 5

Best Known (118−55, 118, s)-Nets in Base 5

(118−55, 118, 132)-Net over F₅ — Constructive and digital

Digital (63, 118, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 59, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(118−55, 118, 151)-Net over F₅ — Digital

Digital (63, 118, 151)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−55, 118, 2899)-Net in Base 5 — Upper bound on s

There is no (63, 118, 2900)-net in base 5, because

1 times m-reduction [i] would yield (63, 117, 2900)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6064 262990 187836 989667 799504 563471 932030 350638 431063 168739 836778 911264 845961 026385 > 5¹¹⁷ [i]