MinT - Best Known (171−67, 171, s)-Nets in Base 4

Best Known (171−67, 171, s)-Nets in Base 4

(171−67, 171, 130)-Net over F₄ — Constructive and digital

Digital (104, 171, 130)-net over F₄, using

25 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(171−67, 171, 273)-Net over F₄ — Digital

Digital (104, 171, 273)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−67, 171, 5516)-Net in Base 4 — Upper bound on s

There is no (104, 171, 5517)-net in base 4, because

1 times m-reduction [i] would yield (104, 170, 5517)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 250877 232839 843872 439914 100674 335075 670210 611917 389227 411154 532040 781062 140260 178346 215248 670783 380256 > 4¹⁷⁰ [i]