MinT - Best Known (152−57, 152, s)-Nets in Base 4

Best Known (152−57, 152, s)-Nets in Base 4

(152−57, 152, 130)-Net over F₄ — Constructive and digital

Digital (95, 152, 130)-net over F₄, using

26 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]

(152−57, 152, 288)-Net over F₄ — Digital

Digital (95, 152, 288)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−57, 152, 6625)-Net in Base 4 — Upper bound on s

There is no (95, 152, 6626)-net in base 4, because

1 times m-reduction [i] would yield (95, 151, 6626)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 167172 481662 797063 578788 335868 108329 827072 935498 394922 470126 786613 757615 825515 901238 358216 > 4¹⁵¹ [i]