MinT - Best Known (131−35, 131, s)-Nets in Base 5

Best Known (131−35, 131, s)-Nets in Base 5

(131−35, 131, 408)-Net over F₅ — Constructive and digital

Digital (96, 131, 408)-net over F₅, using

1 times m-reduction [i] based on digital (96, 132, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 66, 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]

(131−35, 131, 1686)-Net over F₅ — Digital

Digital (96, 131, 1686)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−35, 131, 397133)-Net in Base 5 — Upper bound on s

There is no (96, 131, 397134)-net in base 5, because

1 times m-reduction [i] would yield (96, 130, 397134)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 346986 793875 826927 021386 233657 811487 525934 727770 153816 342308 150590 234658 482450 147423 604025 > 5¹³⁰ [i]