MinT - Best Known (145−55, 145, s)-Nets in Base 4

Best Known (145−55, 145, s)-Nets in Base 4

(145−55, 145, 130)-Net over F₄ — Constructive and digital

Digital (90, 145, 130)-net over F₄, using

23 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(145−55, 145, 267)-Net over F₄ — Digital

Digital (90, 145, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−55, 145, 5897)-Net in Base 4 — Upper bound on s

There is no (90, 145, 5898)-net in base 4, because

1 times m-reduction [i] would yield (90, 144, 5898)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 498 786792 816986 220932 005043 001606 454653 101698 818852 595868 439553 275835 284531 665006 657152 > 4¹⁴⁴ [i]