MinT - Best Known (135−51, 135, s)-Nets in Base 5

Best Known (135−51, 135, s)-Nets in Base 5

(135−51, 135, 252)-Net over F₅ — Constructive and digital

Digital (84, 135, 252)-net over F₅, using

13 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 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]

(135−51, 135, 362)-Net over F₅ — Digital

Digital (84, 135, 362)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−51, 135, 14173)-Net in Base 5 — Upper bound on s

There is no (84, 135, 14174)-net in base 5, because

1 times m-reduction [i] would yield (84, 134, 14174)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4593 344011 193649 202533 493883 429393 875465 732335 913991 924829 867466 247620 646171 995086 045401 708409 > 5¹³⁴ [i]