MinT - Best Known (135−53, 135, s)-Nets in Base 5

Best Known (135−53, 135, s)-Nets in Base 5

(135−53, 135, 252)-Net over F₅ — Constructive and digital

Digital (82, 135, 252)-net over F₅, using

9 times m-reduction [i] based on digital (82, 144, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 72, 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]

(135−53, 135, 313)-Net over F₅ — Digital

Digital (82, 135, 313)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−53, 135, 10539)-Net in Base 5 — Upper bound on s

There is no (82, 135, 10540)-net in base 5, because

1 times m-reduction [i] would yield (82, 134, 10540)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4593 250826 186756 916807 196187 974435 262525 478844 258231 942724 940412 662691 292122 428157 173588 374849 > 5¹³⁴ [i]