MinT - Best Known (179−73, 179, s)-Nets in Base 3

Best Known (179−73, 179, s)-Nets in Base 3

(179−73, 179, 128)-Net over F₃ — Constructive and digital

Digital (106, 179, 128)-net over F₃, using

7 times m-reduction [i] based on digital (106, 186, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 93, 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]

(179−73, 179, 161)-Net over F₃ — Digital

Digital (106, 179, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−73, 179, 1597)-Net in Base 3 — Upper bound on s

There is no (106, 179, 1598)-net in base 3, because

1 times m-reduction [i] would yield (106, 178, 1598)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 625528 786033 050180 285273 036895 057653 378622 695156 130745 394395 663647 168500 475824 149833 > 3¹⁷⁸ [i]