MinT - Best Known (130−52, 130, s)-Nets in Base 4

Best Known (130−52, 130, s)-Nets in Base 4

(130−52, 130, 130)-Net over F₄ — Constructive and digital

Digital (78, 130, 130)-net over F₄, using

14 times m-reduction [i] based on digital (78, 144, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 72, 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]

(130−52, 130, 203)-Net over F₄ — Digital

Digital (78, 130, 203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−52, 130, 3580)-Net in Base 4 — Upper bound on s

There is no (78, 130, 3581)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 862270 492860 097231 433337 538859 973704 950037 383804 660767 789896 019594 099927 446502 > 4¹³⁰ [i]