MinT - Best Known (123−49, 123, s)-Nets in Base 4

Best Known (123−49, 123, s)-Nets in Base 4

(123−49, 123, 130)-Net over F₄ — Constructive and digital

Digital (74, 123, 130)-net over F₄, using

13 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]

(123−49, 123, 197)-Net over F₄ — Digital

Digital (74, 123, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−49, 123, 3736)-Net in Base 4 — Upper bound on s

There is no (74, 123, 3737)-net in base 4, because

1 times m-reduction [i] would yield (74, 122, 3737)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 372517 265294 305899 833217 095008 140482 750577 908851 037460 371295 468478 225449 > 4¹²² [i]