MinT - Best Known (80, 80+69, s)-Nets in Base 5

Best Known (80, 80+69, s)-Nets in Base 5

(80, 80+69, 132)-Net over F₅ — Constructive and digital

Digital (80, 149, 132)-net over F₅, using

t-expansion [i] based on digital (79, 149, 132)-net over F₅, using
- 1 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]

(80, 80+69, 188)-Net over F₅ — Digital

Digital (80, 149, 188)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+69, 3707)-Net in Base 5 — Upper bound on s

There is no (80, 149, 3708)-net in base 5, because

1 times m-reduction [i] would yield (80, 148, 3708)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 158582 394244 097478 363020 546340 617720 437632 247440 954154 696644 145510 896227 132295 524523 638041 865707 970625 > 5¹⁴⁸ [i]