MinT - Best Known (135−47, 135, s)-Nets in Base 5

Best Known (135−47, 135, s)-Nets in Base 5

(135−47, 135, 296)-Net over F₅ — Constructive and digital

Digital (88, 135, 296)-net over F₅, using

3 times m-reduction [i] based on digital (88, 138, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 69, 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]

(135−47, 135, 504)-Net over F₅ — Digital

Digital (88, 135, 504)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−47, 135, 27822)-Net in Base 5 — Upper bound on s

There is no (88, 135, 27823)-net in base 5, because

1 times m-reduction [i] would yield (88, 134, 27823)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4593 954432 882540 768298 389342 786592 343921 118556 971372 167270 049905 909820 470473 858343 754170 692965 > 5¹³⁴ [i]