MinT - Best Known (126, 126+53, s)-Nets in Base 3

Best Known (126, 126+53, s)-Nets in Base 3

(126, 126+53, 228)-Net over F₃ — Constructive and digital

Digital (126, 179, 228)-net over F₃, using

1 times m-reduction [i] based on digital (126, 180, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 60, 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]

(126, 126+53, 420)-Net over F₃ — Digital

Digital (126, 179, 420)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+53, 9717)-Net in Base 3 — Upper bound on s

There is no (126, 179, 9718)-net in base 3, because

1 times m-reduction [i] would yield (126, 178, 9718)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 466780 439261 925691 047103 101584 897345 132934 809234 032384 607415 327953 363590 994814 419773 > 3¹⁷⁸ [i]