MinT - Best Known (91, 91+56, s)-Nets in Base 4

Best Known (91, 91+56, s)-Nets in Base 4

(91, 91+56, 130)-Net over F₄ — Constructive and digital

Digital (91, 147, 130)-net over F₄, using

23 times m-reduction [i] based on digital (91, 170, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 85, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(91, 91+56, 266)-Net over F₄ — Digital

Digital (91, 147, 266)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+56, 5430)-Net in Base 4 — Upper bound on s

There is no (91, 147, 5431)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31829 118019 024897 023119 615342 193554 048763 635149 584602 911442 645357 758632 064153 043872 144300 > 4¹⁴⁷ [i]