MinT - Best Known (138−65, 138, s)-Nets in Base 5

Best Known (138−65, 138, s)-Nets in Base 5

(138−65, 138, 132)-Net over F₅ — Constructive and digital

Digital (73, 138, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 69, 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]

(138−65, 138, 166)-Net over F₅ — Digital

Digital (73, 138, 166)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−65, 138, 3119)-Net in Base 5 — Upper bound on s

There is no (73, 138, 3120)-net in base 5, because

1 times m-reduction [i] would yield (73, 137, 3120)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 579031 154515 811270 131516 937572 522899 040569 566585 562432 998515 987328 760160 971023 925183 663602 180097 > 5¹³⁷ [i]