MinT - Best Known (69, 103, s)-Nets in Base 4

Best Known (69, 103, s)-Nets in Base 4

(69, 103, 195)-Net over F₄ — Constructive and digital

Digital (69, 103, 195)-net over F₄, using

4¹ times duplication [i] based on digital (68, 102, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 34, 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]

(69, 103, 333)-Net over F₄ — Digital

Digital (69, 103, 333)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 103, 10617)-Net in Base 4 — Upper bound on s

There is no (69, 103, 10618)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 102 851603 353227 339339 655811 609890 094290 502027 011003 686212 771011 > 4¹⁰³ [i]