MinT - Best Known (219−120, 219, s)-Nets in Base 4

Best Known (219−120, 219, s)-Nets in Base 4

(219−120, 219, 104)-Net over F₄ — Constructive and digital

Digital (99, 219, 104)-net over F₄, using

t-expansion [i] based on digital (73, 219, 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]

(219−120, 219, 144)-Net over F₄ — Digital

Digital (99, 219, 144)-net over F₄, using

t-expansion [i] based on digital (91, 219, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(219−120, 219, 1169)-Net in Base 4 — Upper bound on s

There is no (99, 219, 1170)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 727668 358273 296013 609855 979822 162994 352578 759996 400930 300004 852868 935985 464682 590640 451735 365014 162208 857105 985506 376587 413758 130720 > 4²¹⁹ [i]