MinT - Best Known (130, 130+93, s)-Nets in Base 3

Best Known (130, 130+93, s)-Nets in Base 3

(130, 130+93, 148)-Net over F₃ — Constructive and digital

Digital (130, 223, 148)-net over F₃, using

3 times m-reduction [i] based on digital (130, 226, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 113, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(130, 130+93, 183)-Net over F₃ — Digital

Digital (130, 223, 183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+93, 1761)-Net in Base 3 — Upper bound on s

There is no (130, 223, 1762)-net in base 3, because

1 times m-reduction [i] would yield (130, 222, 1762)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8456 678212 799534 879524 047131 561636 919700 081412 403570 407355 848769 501269 306287 602625 694922 379218 414719 750925 > 3²²² [i]