MinT - Best Known (53, 79, s)-Nets in Base 4

Best Known (53, 79, s)-Nets in Base 4

(53, 79, 195)-Net over F₄ — Constructive and digital

Digital (53, 79, 195)-net over F₄, using

4¹ times duplication [i] based on digital (52, 78, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 26, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(53, 79, 280)-Net over F₄ — Digital

Digital (53, 79, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 79, 8598)-Net in Base 4 — Upper bound on s

There is no (53, 79, 8599)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 365507 777211 737135 185597 737184 103731 566377 563132 > 4⁷⁹ [i]