MinT - Best Known (84, 84+50, s)-Nets in Base 4

Best Known (84, 84+50, s)-Nets in Base 4

(84, 84+50, 130)-Net over F₄ — Constructive and digital

Digital (84, 134, 130)-net over F₄, using

22 times m-reduction [i] based on digital (84, 156, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 78, 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]

(84, 84+50, 263)-Net over F₄ — Digital

Digital (84, 134, 263)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+50, 5701)-Net in Base 4 — Upper bound on s

There is no (84, 134, 5702)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 474 965174 370141 562924 408221 918597 081563 264242 167924 707031 411727 918677 461534 714728 > 4¹³⁴ [i]