MinT - Best Known (148−56, 148, s)-Nets in Base 4

Best Known (148−56, 148, s)-Nets in Base 4

(148−56, 148, 130)-Net over F₄ — Constructive and digital

Digital (92, 148, 130)-net over F₄, using

24 times m-reduction [i] based on digital (92, 172, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 86, 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]

(148−56, 148, 274)-Net over F₄ — Digital

Digital (92, 148, 274)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−56, 148, 5707)-Net in Base 4 — Upper bound on s

There is no (92, 148, 5708)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127431 845936 121012 683430 370315 889891 896574 922420 195708 462558 583177 748554 825527 891389 086480 > 4¹⁴⁸ [i]