MinT - Best Known (245−142, 245, s)-Nets in Base 4

Best Known (245−142, 245, s)-Nets in Base 4

(245−142, 245, 104)-Net over F₄ — Constructive and digital

Digital (103, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 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]

(245−142, 245, 144)-Net over F₄ — Digital

Digital (103, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 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]

(245−142, 245, 1029)-Net in Base 4 — Upper bound on s

There is no (103, 245, 1030)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3405 625664 018264 513696 788712 580600 842693 787680 505769 428852 025638 506714 250333 385692 715260 812140 997522 331636 033217 971911 785058 130119 065737 405738 069760 > 4²⁴⁵ [i]