MinT - Best Known (194−94, 194, s)-Nets in Base 4

Best Known (194−94, 194, s)-Nets in Base 4

(194−94, 194, 104)-Net over F₄ — Constructive and digital

Digital (100, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(194−94, 194, 155)-Net over F₄ — Digital

Digital (100, 194, 155)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−94, 194, 1832)-Net in Base 4 — Upper bound on s

There is no (100, 194, 1833)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 636 021196 888802 412518 793534 166237 204933 384878 129892 711144 835296 546712 143970 326782 855044 705814 307832 618087 423462 377216 > 4¹⁹⁴ [i]