MinT - Best Known (245−112, 245, s)-Nets in Base 4

Best Known (245−112, 245, s)-Nets in Base 4

(245−112, 245, 130)-Net over F₄ — Constructive and digital

Digital (133, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(245−112, 245, 228)-Net over F₄ — Digital

Digital (133, 245, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−112, 245, 3069)-Net in Base 4 — Upper bound on s

There is no (133, 245, 3070)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3218 504391 224156 815215 452911 848723 382275 690863 648156 715961 971119 352720 393685 895271 260425 711602 778319 322493 988642 073131 805473 087706 663576 362647 783669 > 4²⁴⁵ [i]