MinT - Best Known (122−57, 122, s)-Nets in Base 5

Best Known (122−57, 122, s)-Nets in Base 5

(122−57, 122, 132)-Net over F₅ — Constructive and digital

Digital (65, 122, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 61, 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]

(122−57, 122, 154)-Net over F₅ — Digital

Digital (65, 122, 154)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−57, 122, 2940)-Net in Base 5 — Upper bound on s

There is no (65, 122, 2941)-net in base 5, because

1 times m-reduction [i] would yield (65, 121, 2941)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 764083 638310 999681 940449 807660 079899 436194 933614 743435 469224 135516 417176 582950 781585 > 5¹²¹ [i]