MinT - Best Known (140−61, 140, s)-Nets in Base 4

Best Known (140−61, 140, s)-Nets in Base 4

(140−61, 140, 130)-Net over F₄ — Constructive and digital

Digital (79, 140, 130)-net over F₄, using

6 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]

(140−61, 140, 163)-Net over F₄ — Digital

Digital (79, 140, 163)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−61, 140, 2448)-Net in Base 4 — Upper bound on s

There is no (79, 140, 2449)-net in base 4, because

1 times m-reduction [i] would yield (79, 139, 2449)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 488479 193718 228243 347699 702430 660916 347709 966670 242676 823115 791215 780162 628564 473920 > 4¹³⁹ [i]