MinT - Best Known (137−58, 137, s)-Nets in Base 4

Best Known (137−58, 137, s)-Nets in Base 4

(137−58, 137, 130)-Net over F₄ — Constructive and digital

Digital (79, 137, 130)-net over F₄, using

9 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]

(137−58, 137, 176)-Net over F₄ — Digital

Digital (79, 137, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−58, 137, 2694)-Net in Base 4 — Upper bound on s

There is no (79, 137, 2695)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30615 053646 306529 838100 377124 269143 760958 224209 770987 746007 793140 829293 450907 108000 > 4¹³⁷ [i]