MinT - Best Known (148−42, 148, s)-Nets in Base 4

Best Known (148−42, 148, s)-Nets in Base 4

(148−42, 148, 531)-Net over F₄ — Constructive and digital

Digital (106, 148, 531)-net over F₄, using

4¹ times duplication [i] based on digital (105, 147, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 49, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(148−42, 148, 822)-Net over F₄ — Digital

Digital (106, 148, 822)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−42, 148, 50619)-Net in Base 4 — Upper bound on s

There is no (106, 148, 50620)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127358 919620 338578 929634 014413 276422 752623 676434 969236 177857 810021 384787 777642 391097 110354 > 4¹⁴⁸ [i]