MinT - Best Known (79, 79+47, s)-Nets in Base 4

Best Known (79, 79+47, s)-Nets in Base 4

(79, 79+47, 130)-Net over F₄ — Constructive and digital

Digital (79, 126, 130)-net over F₄, using

20 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+47, 250)-Net over F₄ — Digital

Digital (79, 126, 250)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+47, 5861)-Net in Base 4 — Upper bound on s

There is no (79, 126, 5862)-net in base 4, because

1 times m-reduction [i] would yield (79, 125, 5862)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1811 617930 845672 637295 704083 193260 609738 745071 789645 198556 473579 728252 599408 > 4¹²⁵ [i]