MinT - Best Known (184−79, 184, s)-Nets in Base 3

Best Known (184−79, 184, s)-Nets in Base 3

(184−79, 184, 128)-Net over F₃ — Constructive and digital

Digital (105, 184, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 92, 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]

(184−79, 184, 143)-Net over F₃ — Digital

Digital (105, 184, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−79, 184, 1296)-Net in Base 3 — Upper bound on s

There is no (105, 184, 1297)-net in base 3, because

1 times m-reduction [i] would yield (105, 183, 1297)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2113 047851 989303 737619 627438 813208 870775 335303 642156 307945 231212 722485 320021 231319 367755 > 3¹⁸³ [i]