MinT - Best Known (80, 80+45, s)-Nets in Base 5

Best Known (80, 80+45, s)-Nets in Base 5

(80, 80+45, 252)-Net over F₅ — Constructive and digital

Digital (80, 125, 252)-net over F₅, using

15 times m-reduction [i] based on digital (80, 140, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 70, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(80, 80+45, 412)-Net over F₅ — Digital

Digital (80, 125, 412)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+45, 19682)-Net in Base 5 — Upper bound on s

There is no (80, 125, 19683)-net in base 5, because

1 times m-reduction [i] would yield (80, 124, 19683)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 470 243616 881109 283539 859507 377129 060339 452366 790246 100118 300656 639913 702369 764313 780905 > 5¹²⁴ [i]