MinT - Best Known (178−75, 178, s)-Nets in Base 3

Best Known (178−75, 178, s)-Nets in Base 3

(178−75, 178, 128)-Net over F₃ — Constructive and digital

Digital (103, 178, 128)-net over F₃, using

2 times m-reduction [i] based on digital (103, 180, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 90, 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]

(178−75, 178, 146)-Net over F₃ — Digital

Digital (103, 178, 146)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−75, 178, 1367)-Net in Base 3 — Upper bound on s

There is no (103, 178, 1368)-net in base 3, because

1 times m-reduction [i] would yield (103, 177, 1368)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 839280 665646 079886 128314 118105 566006 005047 732804 871521 729072 691979 549336 404748 454449 > 3¹⁷⁷ [i]