MinT - Best Known (91, 164, s)-Nets in Base 4

Best Known (91, 164, s)-Nets in Base 4

(91, 164, 130)-Net over F₄ — Constructive and digital

Digital (91, 164, 130)-net over F₄, using

6 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, 164, 175)-Net over F₄ — Digital

Digital (91, 164, 175)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 164, 2503)-Net in Base 4 — Upper bound on s

There is no (91, 164, 2504)-net in base 4, because

1 times m-reduction [i] would yield (91, 163, 2504)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 137 712777 127879 051870 488917 633269 877548 597971 425827 293409 848763 352419 794856 940846 040561 175351 204702 > 4¹⁶³ [i]