MinT - Best Known (80, 80+54, s)-Nets in Base 5

Best Known (80, 80+54, s)-Nets in Base 5

(80, 80+54, 252)-Net over F₅ — Constructive and digital

Digital (80, 134, 252)-net over F₅, using

6 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+54, 283)-Net over F₅ — Digital

Digital (80, 134, 283)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+54, 8021)-Net in Base 5 — Upper bound on s

There is no (80, 134, 8022)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4603 381264 376542 394382 518679 186500 085322 894114 350323 622081 250360 807331 273467 603127 602207 957625 > 5¹³⁴ [i]