MinT - Best Known (61, 61+30, s)-Nets in Base 4

Best Known (61, 61+30, s)-Nets in Base 4

(61, 61+30, 195)-Net over F₄ — Constructive and digital

Digital (61, 91, 195)-net over F₄, using

4¹ times duplication [i] based on digital (60, 90, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 30, 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]

(61, 61+30, 306)-Net over F₄ — Digital

Digital (61, 91, 306)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+30, 9607)-Net in Base 4 — Upper bound on s

There is no (61, 91, 9608)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 136791 253075 162282 329201 219847 129823 206871 324768 944528 > 4⁹¹ [i]