MinT - Best Known (95, 95+77, s)-Nets in Base 4

Best Known (95, 95+77, s)-Nets in Base 4

(95, 95+77, 130)-Net over F₄ — Constructive and digital

Digital (95, 172, 130)-net over F₄, using

6 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(95, 95+77, 179)-Net over F₄ — Digital

Digital (95, 172, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 95+77, 2533)-Net in Base 4 — Upper bound on s

There is no (95, 172, 2534)-net in base 4, because

1 times m-reduction [i] would yield (95, 171, 2534)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 068826 304044 187521 908237 813693 025425 080463 208102 000769 303491 154724 680537 937224 374327 960775 895385 912520 > 4¹⁷¹ [i]