MinT - Best Known (178−77, 178, s)-Nets in Base 4

Best Known (178−77, 178, s)-Nets in Base 4

(178−77, 178, 130)-Net over F₄ — Constructive and digital

Digital (101, 178, 130)-net over F₄, using

12 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(178−77, 178, 206)-Net over F₄ — Digital

Digital (101, 178, 206)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−77, 178, 3160)-Net in Base 4 — Upper bound on s

There is no (101, 178, 3161)-net in base 4, because

1 times m-reduction [i] would yield (101, 177, 3161)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36875 518422 661468 348636 446307 292960 255049 799322 180472 093605 499672 683983 591595 939426 409420 062361 037984 062664 > 4¹⁷⁷ [i]