MinT - Best Known (223−46, 223, s)-Nets in Base 4

Best Known (223−46, 223, s)-Nets in Base 4

(223−46, 223, 1539)-Net over F₄ — Constructive and digital

Digital (177, 223, 1539)-net over F₄, using

4¹ times duplication [i] based on digital (176, 222, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 74, 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]

(223−46, 223, 5679)-Net over F₄ — Digital

Digital (177, 223, 5679)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−46, 223, 2161202)-Net in Base 4 — Upper bound on s

There is no (177, 223, 2161203)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 709914 338650 479380 331097 287045 310768 682572 985942 166276 428448 509406 708147 182945 870359 719304 083274 647758 783745 771136 335885 506190 118080 > 4²²³ [i]