MinT - Best Known (79, 79+57, s)-Nets in Base 4

Best Known (79, 79+57, s)-Nets in Base 4

(79, 79+57, 130)-Net over F₄ — Constructive and digital

Digital (79, 136, 130)-net over F₄, using

10 times m-reduction [i] based on digital (79, 146, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 73, 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]

(79, 79+57, 180)-Net over F₄ — Digital

Digital (79, 136, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+57, 2987)-Net in Base 4 — Upper bound on s

There is no (79, 136, 2988)-net in base 4, because

1 times m-reduction [i] would yield (79, 135, 2988)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1897 642001 193439 323145 325897 896067 650355 467447 125817 637275 316727 950300 824501 287160 > 4¹³⁵ [i]