MinT - Best Known (90, 90+78, s)-Nets in Base 4

Best Known (90, 90+78, s)-Nets in Base 4

(90, 90+78, 130)-Net over F₄ — Constructive and digital

Digital (90, 168, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 84, 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]

(90, 90+78, 156)-Net over F₄ — Digital

Digital (90, 168, 156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+78, 1980)-Net in Base 4 — Upper bound on s

There is no (90, 168, 1981)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140095 247206 702332 868222 966062 440246 129664 576250 461012 210588 420931 359321 482153 965944 273290 419951 431640 > 4¹⁶⁸ [i]