MinT - Best Known (135−58, 135, s)-Nets in Base 4

Best Known (135−58, 135, s)-Nets in Base 4

(135−58, 135, 130)-Net over F₄ — Constructive and digital

Digital (77, 135, 130)-net over F₄, using

7 times m-reduction [i] based on digital (77, 142, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 71, 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]

(135−58, 135, 166)-Net over F₄ — Digital

Digital (77, 135, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−58, 135, 2446)-Net in Base 4 — Upper bound on s

There is no (77, 135, 2447)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1910 494481 907184 786979 963616 207284 807748 764095 239184 718952 089033 636561 977397 300560 > 4¹³⁵ [i]