MinT - Best Known (177−79, 177, s)-Nets in Base 3

Best Known (177−79, 177, s)-Nets in Base 3

(177−79, 177, 80)-Net over F₃ — Constructive and digital

Digital (98, 177, 80)-net over F₃, using

3 times m-reduction [i] based on digital (98, 180, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 90, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(177−79, 177, 124)-Net over F₃ — Digital

Digital (98, 177, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−79, 177, 1057)-Net in Base 3 — Upper bound on s

There is no (98, 177, 1058)-net in base 3, because

1 times m-reduction [i] would yield (98, 176, 1058)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 960205 398395 380754 020109 402919 422294 318473 972051 257645 516164 880278 761734 951749 494953 > 3¹⁷⁶ [i]