MinT - Best Known (111, 111+92, s)-Nets in Base 4

Best Known (111, 111+92, s)-Nets in Base 4

(111, 111+92, 130)-Net over F₄ — Constructive and digital

Digital (111, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(111, 111+92, 198)-Net over F₄ — Digital

Digital (111, 203, 198)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+92, 2685)-Net in Base 4 — Upper bound on s

There is no (111, 203, 2686)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 167 435412 338370 259828 274090 405989 979624 845067 498210 902371 930657 412079 084270 027746 010542 014560 339707 533704 441973 493869 695440 > 4²⁰³ [i]