MinT - Best Known (130−57, 130, s)-Nets in Base 5

Best Known (130−57, 130, s)-Nets in Base 5

(130−57, 130, 132)-Net over F₅ — Constructive and digital

Digital (73, 130, 132)-net over F₅, using

8 times m-reduction [i] based on digital (73, 138, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 69, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(130−57, 130, 203)-Net over F₅ — Digital

Digital (73, 130, 203)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−57, 130, 4669)-Net in Base 5 — Upper bound on s

There is no (73, 130, 4670)-net in base 5, because

1 times m-reduction [i] would yield (73, 129, 4670)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 470929 033675 522297 162657 547544 023856 305168 229348 525068 194506 292148 933024 789317 230497 998529 > 5¹²⁹ [i]