MinT - Best Known (177−73, 177, s)-Nets in Base 4

Best Known (177−73, 177, s)-Nets in Base 4

(177−73, 177, 130)-Net over F₄ — Constructive and digital

Digital (104, 177, 130)-net over F₄, using

19 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]

(177−73, 177, 238)-Net over F₄ — Digital

Digital (104, 177, 238)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−73, 177, 4149)-Net in Base 4 — Upper bound on s

There is no (104, 177, 4150)-net in base 4, because

1 times m-reduction [i] would yield (104, 176, 4150)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9247 154177 874092 576937 088128 537445 364952 479813 534168 499174 833161 956145 083462 937836 483278 971452 730748 178079 > 4¹⁷⁶ [i]