MinT - Best Known (130−51, 130, s)-Nets in Base 5

Best Known (130−51, 130, s)-Nets in Base 5

(130−51, 130, 252)-Net over F₅ — Constructive and digital

Digital (79, 130, 252)-net over F₅, using

8 times m-reduction [i] based on digital (79, 138, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 69, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(130−51, 130, 304)-Net over F₅ — Digital

Digital (79, 130, 304)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−51, 130, 10267)-Net in Base 5 — Upper bound on s

There is no (79, 130, 10268)-net in base 5, because

1 times m-reduction [i] would yield (79, 129, 10268)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469835 425042 827709 625041 515578 242351 476025 683532 411261 222037 609563 076779 592601 363002 295665 > 5¹²⁹ [i]