MinT - Best Known (217−126, 217, s)-Nets in Base 4

Best Known (217−126, 217, s)-Nets in Base 4

(217−126, 217, 104)-Net over F₄ — Constructive and digital

Digital (91, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(217−126, 217, 144)-Net over F₄ — Digital

Digital (91, 217, 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]

(217−126, 217, 909)-Net in Base 4 — Upper bound on s

There is no (91, 217, 910)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46956 238945 259709 179861 242791 433482 070866 467816 657295 590890 159618 676903 127743 483266 872302 572930 845152 364204 412932 939037 939719 052480 > 4²¹⁷ [i]