MinT - Best Known (131−43, 131, s)-Nets in Base 5

Best Known (131−43, 131, s)-Nets in Base 5

(131−43, 131, 296)-Net over F₅ — Constructive and digital

Digital (88, 131, 296)-net over F₅, using

7 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]

(131−43, 131, 638)-Net over F₅ — Digital

Digital (88, 131, 638)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−43, 131, 46051)-Net in Base 5 — Upper bound on s

There is no (88, 131, 46052)-net in base 5, because

1 times m-reduction [i] would yield (88, 130, 46052)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 347736 721671 249667 499085 279048 430522 518356 987414 136004 806728 235697 332851 779620 447042 645265 > 5¹³⁰ [i]