MinT - Best Known (121−54, 121, s)-Nets in Base 4

Best Known (121−54, 121, s)-Nets in Base 4

(121−54, 121, 130)-Net over F₄ — Constructive and digital

Digital (67, 121, 130)-net over F₄, using

1 times m-reduction [i] based on digital (67, 122, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(121−54, 121, 134)-Net over F₄ — Digital

Digital (67, 121, 134)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−54, 121, 1795)-Net in Base 4 — Upper bound on s

There is no (67, 121, 1796)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 139517 580171 820436 244857 106995 191409 477460 009471 049888 899539 520748 825632 > 4¹²¹ [i]