MinT - Best Known (93, 93+71, s)-Nets in Base 4

Best Known (93, 93+71, s)-Nets in Base 4

(93, 93+71, 130)-Net over F₄ — Constructive and digital

Digital (93, 164, 130)-net over F₄, using

10 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 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]

(93, 93+71, 191)-Net over F₄ — Digital

Digital (93, 164, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+71, 2922)-Net in Base 4 — Upper bound on s

There is no (93, 164, 2923)-net in base 4, because

1 times m-reduction [i] would yield (93, 163, 2923)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 137 031244 855919 754048 221850 876732 888030 971318 030976 983851 343732 265044 263637 241487 407185 291302 538092 > 4¹⁶³ [i]