MinT - Best Known (260−168, 260, s)-Nets in Base 4

Best Known (260−168, 260, s)-Nets in Base 4

(260−168, 260, 104)-Net over F₄ — Constructive and digital

Digital (92, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−168, 260, 144)-Net over F₄ — Digital

Digital (92, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 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]

(260−168, 260, 713)-Net in Base 4 — Upper bound on s

There is no (92, 260, 714)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 564756 771419 536964 840245 180861 367955 527005 156928 596487 911070 010793 652910 164085 776357 183367 116763 816037 979332 338479 465184 000645 210724 205718 461359 029299 628400 > 4²⁶⁰ [i]