MinT - Best Known (135−43, 135, s)-Nets in Base 5

Best Known (135−43, 135, s)-Nets in Base 5

(135−43, 135, 296)-Net over F₅ — Constructive and digital

Digital (92, 135, 296)-net over F₅, using

11 times m-reduction [i] based on digital (92, 146, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 73, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(135−43, 135, 749)-Net over F₅ — Digital

Digital (92, 135, 749)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−43, 135, 62577)-Net in Base 5 — Upper bound on s

There is no (92, 135, 62578)-net in base 5, because

1 times m-reduction [i] would yield (92, 134, 62578)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4591 908745 835092 054411 194282 953231 904070 686227 480357 139752 905522 960176 073256 411860 674321 580745 > 5¹³⁴ [i]