MinT - Best Known (128, 128+51, s)-Nets in Base 3

Best Known (128, 128+51, s)-Nets in Base 3

(128, 128+51, 252)-Net over F₃ — Constructive and digital

Digital (128, 179, 252)-net over F₃, using

1 times m-reduction [i] based on digital (128, 180, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 60, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(128, 128+51, 478)-Net over F₃ — Digital

Digital (128, 179, 478)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+51, 12672)-Net in Base 3 — Upper bound on s

There is no (128, 179, 12673)-net in base 3, because

1 times m-reduction [i] would yield (128, 178, 12673)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 473110 410269 296986 671413 401729 575314 211591 724569 090782 061244 543735 566245 088219 411875 > 3¹⁷⁸ [i]