MinT - Best Known (55, 55+47, s)-Nets in Base 5

Best Known (55, 55+47, s)-Nets in Base 5

(55, 55+47, 132)-Net over F₅ — Constructive and digital

Digital (55, 102, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 51, 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]

(55, 55+47, 140)-Net over F₅ — Digital

Digital (55, 102, 140)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+47, 2748)-Net in Base 5 — Upper bound on s

There is no (55, 102, 2749)-net in base 5, because

1 times m-reduction [i] would yield (55, 101, 2749)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 39486 712114 428824 847739 982996 238079 168564 198527 126955 485510 524115 210909 > 5¹⁰¹ [i]