MinT - Best Known (155−59, 155, s)-Nets in Base 4

Best Known (155−59, 155, s)-Nets in Base 4

(155−59, 155, 130)-Net over F₄ — Constructive and digital

Digital (96, 155, 130)-net over F₄, using

25 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(155−59, 155, 278)-Net over F₄ — Digital

Digital (96, 155, 278)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−59, 155, 6101)-Net in Base 4 — Upper bound on s

There is no (96, 155, 6102)-net in base 4, because

1 times m-reduction [i] would yield (96, 154, 6102)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 618348 134998 143547 187149 382485 405509 401808 068647 050232 753134 048318 520062 391185 722058 604184 > 4¹⁵⁴ [i]