MinT - Best Known (106−32, 106, s)-Nets in Base 4

Best Known (106−32, 106, s)-Nets in Base 4

(106−32, 106, 312)-Net over F₄ — Constructive and digital

Digital (74, 106, 312)-net over F₄, using

4¹ times duplication [i] based on digital (73, 105, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 35, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(106−32, 106, 489)-Net over F₄ — Digital

Digital (74, 106, 489)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−32, 106, 22070)-Net in Base 4 — Upper bound on s

There is no (74, 106, 22071)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6584 320226 273641 328264 898318 457210 465717 742951 582641 867985 029819 > 4¹⁰⁶ [i]