MinT - Best Known (91, 91+62, s)-Nets in Base 4

Best Known (91, 91+62, s)-Nets in Base 4

(91, 91+62, 130)-Net over F₄ — Constructive and digital

Digital (91, 153, 130)-net over F₄, using

17 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+62, 222)-Net over F₄ — Digital

Digital (91, 153, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+62, 3850)-Net in Base 4 — Upper bound on s

There is no (91, 153, 3851)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 789074 225556 441537 623621 234873 773901 692989 792752 470420 967855 368072 428984 775088 416852 087296 > 4¹⁵³ [i]