MinT - Best Known (133−53, 133, s)-Nets in Base 5

Best Known (133−53, 133, s)-Nets in Base 5

(133−53, 133, 252)-Net over F₅ — Constructive and digital

Digital (80, 133, 252)-net over F₅, using

7 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]

(133−53, 133, 293)-Net over F₅ — Digital

Digital (80, 133, 293)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−53, 133, 9310)-Net in Base 5 — Upper bound on s

There is no (80, 133, 9311)-net in base 5, because

1 times m-reduction [i] would yield (80, 132, 9311)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 184 012226 169135 189563 658819 219256 420469 881271 693494 364246 001832 810763 547400 519182 535405 119385 > 5¹³² [i]