MinT - Best Known (145−57, 145, s)-Nets in Base 3

Best Known (145−57, 145, s)-Nets in Base 3

(145−57, 145, 128)-Net over F₃ — Constructive and digital

Digital (88, 145, 128)-net over F₃, using

5 times m-reduction [i] based on digital (88, 150, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 75, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(145−57, 145, 150)-Net over F₃ — Digital

Digital (88, 145, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−57, 145, 1578)-Net in Base 3 — Upper bound on s

There is no (88, 145, 1579)-net in base 3, because

1 times m-reduction [i] would yield (88, 144, 1579)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 510 368553 884590 369164 590515 685441 739409 937911 286468 561270 608236 306345 > 3¹⁴⁴ [i]