MinT - Best Known (171−51, 171, s)-Nets in Base 3

Best Known (171−51, 171, s)-Nets in Base 3

(171−51, 171, 228)-Net over F₃ — Constructive and digital

Digital (120, 171, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 57, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(171−51, 171, 395)-Net over F₃ — Digital

Digital (120, 171, 395)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−51, 171, 8909)-Net in Base 3 — Upper bound on s

There is no (120, 171, 8910)-net in base 3, because

1 times m-reduction [i] would yield (120, 170, 8910)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1293 678780 392233 381318 706317 603989 744520 577459 124223 930152 749283 152801 360799 041005 > 3¹⁷⁰ [i]