MinT - Best Known (167−71, 167, s)-Nets in Base 4

Best Known (167−71, 167, s)-Nets in Base 4

(167−71, 167, 130)-Net over F₄ — Constructive and digital

Digital (96, 167, 130)-net over F₄, using

13 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(167−71, 167, 205)-Net over F₄ — Digital

Digital (96, 167, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−71, 167, 3295)-Net in Base 4 — Upper bound on s

There is no (96, 167, 3296)-net in base 4, because

1 times m-reduction [i] would yield (96, 166, 3296)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8825 986702 641902 291735 958785 476106 446963 645194 895825 801055 148392 240134 244637 519085 160983 850184 955342 > 4¹⁶⁶ [i]