MinT - Best Known (152−59, 152, s)-Nets in Base 4

Best Known (152−59, 152, s)-Nets in Base 4

(152−59, 152, 130)-Net over F₄ — Constructive and digital

Digital (93, 152, 130)-net over F₄, using

22 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 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]

(152−59, 152, 256)-Net over F₄ — Digital

Digital (93, 152, 256)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−59, 152, 5283)-Net in Base 4 — Upper bound on s

There is no (93, 152, 5284)-net in base 4, because

1 times m-reduction [i] would yield (93, 151, 5284)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 167460 543691 740476 454806 602284 723070 954900 116007 297312 891378 741340 526611 541588 226464 607208 > 4¹⁵¹ [i]