MinT - Best Known (135−61, 135, s)-Nets in Base 4

Best Known (135−61, 135, s)-Nets in Base 4

(135−61, 135, 130)-Net over F₄ — Constructive and digital

Digital (74, 135, 130)-net over F₄, using

1 times m-reduction [i] based on digital (74, 136, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 68, 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]

(135−61, 135, 141)-Net over F₄ — Digital

Digital (74, 135, 141)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−61, 135, 1938)-Net in Base 4 — Upper bound on s

There is no (74, 135, 1939)-net in base 4, because

1 times m-reduction [i] would yield (74, 134, 1939)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 478 773205 877060 848789 699331 179662 088213 071470 069384 490200 182924 427399 254491 626080 > 4¹³⁴ [i]