MinT - Best Known (144−68, 144, s)-Nets in Base 5

Best Known (144−68, 144, s)-Nets in Base 5

(144−68, 144, 132)-Net over F₅ — Constructive and digital

Digital (76, 144, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 72, 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]

(144−68, 144, 171)-Net over F₅ — Digital

Digital (76, 144, 171)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−68, 144, 3063)-Net in Base 5 — Upper bound on s

There is no (76, 144, 3064)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45013 170056 911884 058109 892067 693946 724119 468571 785050 173502 718349 180959 001137 565638 939601 547552 113025 > 5¹⁴⁴ [i]