MinT - Best Known (135−49, 135, s)-Nets in Base 5

Best Known (135−49, 135, s)-Nets in Base 5

(135−49, 135, 252)-Net over F₅ — Constructive and digital

Digital (86, 135, 252)-net over F₅, using

t-expansion [i] based on digital (85, 135, 252)-net over F₅, using
- 15 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(135−49, 135, 424)-Net over F₅ — Digital

Digital (86, 135, 424)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−49, 135, 19565)-Net in Base 5 — Upper bound on s

There is no (86, 135, 19566)-net in base 5, because

1 times m-reduction [i] would yield (86, 134, 19566)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4593 023037 680150 665319 294535 428236 120841 431064 365316 504107 609285 595480 963466 635639 186758 455425 > 5¹³⁴ [i]