MinT - Best Known (79, 79+55, s)-Nets in Base 4

Best Known (79, 79+55, s)-Nets in Base 4

(79, 79+55, 130)-Net over F₄ — Constructive and digital

Digital (79, 134, 130)-net over F₄, using

12 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+55, 191)-Net over F₄ — Digital

Digital (79, 134, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+55, 3343)-Net in Base 4 — Upper bound on s

There is no (79, 134, 3344)-net in base 4, because

1 times m-reduction [i] would yield (79, 133, 3344)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 119 448283 243834 054036 623857 758459 712374 513784 961045 437924 117494 709584 702689 050800 > 4¹³³ [i]