MinT - Best Known (197−104, 197, s)-Nets in Base 4

Best Known (197−104, 197, s)-Nets in Base 4

(197−104, 197, 104)-Net over F₄ — Constructive and digital

Digital (93, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(197−104, 197, 144)-Net over F₄ — Digital

Digital (93, 197, 144)-net over F₄, using

t-expansion [i] based on digital (91, 197, 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]

(197−104, 197, 1244)-Net in Base 4 — Upper bound on s

There is no (93, 197, 1245)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40454 137373 186540 984744 254197 524428 959778 580352 776572 191184 628138 803428 739252 020214 464727 676096 101802 914928 485799 339806 > 4¹⁹⁷ [i]