MinT - Best Known (58, 58+37, s)-Nets in Base 4

Best Known (58, 58+37, s)-Nets in Base 4

(58, 58+37, 130)-Net over F₄ — Constructive and digital

Digital (58, 95, 130)-net over F₄, using

9 times m-reduction [i] based on digital (58, 104, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 52, 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]

(58, 58+37, 172)-Net over F₄ — Digital

Digital (58, 95, 172)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+37, 3493)-Net in Base 4 — Upper bound on s

There is no (58, 95, 3494)-net in base 4, because

1 times m-reduction [i] would yield (58, 94, 3494)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 392 623778 196867 869864 610330 241550 891542 733284 525225 899004 > 4⁹⁴ [i]