MinT - Best Known (192−89, 192, s)-Nets in Base 4

Best Known (192−89, 192, s)-Nets in Base 4

(192−89, 192, 130)-Net over F₄ — Constructive and digital

Digital (103, 192, 130)-net over F₄, using

2 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(192−89, 192, 176)-Net over F₄ — Digital

Digital (103, 192, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−89, 192, 2326)-Net in Base 4 — Upper bound on s

There is no (103, 192, 2327)-net in base 4, because

1 times m-reduction [i] would yield (103, 191, 2327)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 018128 411028 106816 351224 748700 136158 653038 185630 230626 579349 446469 922030 168012 203148 823443 988874 681690 151352 648528 > 4¹⁹¹ [i]