MinT - Best Known (144−64, 144, s)-Nets in Base 5

Best Known (144−64, 144, s)-Nets in Base 5

(144−64, 144, 132)-Net over F₅ — Constructive and digital

Digital (80, 144, 132)-net over F₅, using

t-expansion [i] based on digital (79, 144, 132)-net over F₅, using
- 6 times m-reduction [i] based on digital (79, 150, 132)-net over F₅, using
  - trace code for nets [i] based on digital (4, 75, 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]

(144−64, 144, 211)-Net over F₅ — Digital

Digital (80, 144, 211)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−64, 144, 4445)-Net in Base 5 — Upper bound on s

There is no (80, 144, 4446)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45070 977715 949962 421800 222309 502554 518776 763178 526874 951993 123205 947227 474393 693989 421701 130140 491265 > 5¹⁴⁴ [i]