MinT - Best Known (49, 73, s)-Nets in Base 4

Best Known (49, 73, s)-Nets in Base 4

(49, 73, 195)-Net over F₄ — Constructive and digital

Digital (49, 73, 195)-net over F₄, using

4¹ times duplication [i] based on digital (48, 72, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 24, 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]

(49, 73, 267)-Net over F₄ — Digital

Digital (49, 73, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 73, 8095)-Net in Base 4 — Upper bound on s

There is no (49, 73, 8096)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 89 222218 170289 988627 077882 669927 709843 630941 > 4⁷³ [i]