MinT - Best Known (127, 127+55, s)-Nets in Base 3

Best Known (127, 127+55, s)-Nets in Base 3

(127, 127+55, 204)-Net over F₃ — Constructive and digital

Digital (127, 182, 204)-net over F₃, using

1 times m-reduction [i] based on digital (127, 183, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 61, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(127, 127+55, 399)-Net over F₃ — Digital

Digital (127, 182, 399)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+55, 8600)-Net in Base 3 — Upper bound on s

There is no (127, 182, 8601)-net in base 3, because

1 times m-reduction [i] would yield (127, 181, 8601)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 915424 529598 464028 951581 686395 002335 750309 147126 263774 402049 969832 928586 380536 893659 > 3¹⁸¹ [i]