MinT - Best Known (132−35, 132, s)-Nets in Base 5

Best Known (132−35, 132, s)-Nets in Base 5

(132−35, 132, 408)-Net over F₅ — Constructive and digital

Digital (97, 132, 408)-net over F₅, using

2 times m-reduction [i] based on digital (97, 134, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 67, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(132−35, 132, 1767)-Net over F₅ — Digital

Digital (97, 132, 1767)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−35, 132, 436569)-Net in Base 5 — Upper bound on s

There is no (97, 132, 436570)-net in base 5, because

1 times m-reduction [i] would yield (97, 131, 436570)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 734540 009744 578352 129300 588543 943750 640502 534994 397514 059237 608448 564110 485605 704426 577769 > 5¹³¹ [i]