MinT - Best Known (229−48, 229, s)-Nets in Base 4

Best Known (229−48, 229, s)-Nets in Base 4

(229−48, 229, 1539)-Net over F₄ — Constructive and digital

Digital (181, 229, 1539)-net over F₄, using

4¹ times duplication [i] based on digital (180, 228, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 76, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(229−48, 229, 5276)-Net over F₄ — Digital

Digital (181, 229, 5276)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−48, 229, 1815066)-Net in Base 4 — Upper bound on s

There is no (181, 229, 1815067)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744286 741184 804078 332120 668156 613160 477546 666971 104873 169231 833644 369979 656456 308527 726243 783758 638967 240941 355149 156596 831649 579450 185541 > 4²²⁹ [i]