MinT - Best Known (94, 94+77, s)-Nets in Base 4

Best Known (94, 94+77, s)-Nets in Base 4

(94, 94+77, 130)-Net over F₄ — Constructive and digital

Digital (94, 171, 130)-net over F₄, using

5 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(94, 94+77, 174)-Net over F₄ — Digital

Digital (94, 171, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+77, 2441)-Net in Base 4 — Upper bound on s

There is no (94, 171, 2442)-net in base 4, because

1 times m-reduction [i] would yield (94, 170, 2442)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 263170 263665 960791 433612 058326 047122 299160 092610 807682 998291 943463 155854 159404 396897 109784 766127 769040 > 4¹⁷⁰ [i]