MinT - Best Known (142−63, 142, s)-Nets in Base 4

Best Known (142−63, 142, s)-Nets in Base 4

(142−63, 142, 130)-Net over F₄ — Constructive and digital

Digital (79, 142, 130)-net over F₄, using

4 times m-reduction [i] based on digital (79, 146, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 73, 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]

(142−63, 142, 156)-Net over F₄ — Digital

Digital (79, 142, 156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−63, 142, 2241)-Net in Base 4 — Upper bound on s

There is no (79, 142, 2242)-net in base 4, because

1 times m-reduction [i] would yield (79, 141, 2242)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 871752 975872 278427 354754 432337 863029 155729 827035 759900 371824 770554 653383 181883 370976 > 4¹⁴¹ [i]