MinT - Best Known (176−69, 176, s)-Nets in Base 4

Best Known (176−69, 176, s)-Nets in Base 4

(176−69, 176, 130)-Net over F₄ — Constructive and digital

Digital (107, 176, 130)-net over F₄, using

t-expansion [i] based on digital (105, 176, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(176−69, 176, 280)-Net over F₄ — Digital

Digital (107, 176, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−69, 176, 5637)-Net in Base 4 — Upper bound on s

There is no (107, 176, 5638)-net in base 4, because

1 times m-reduction [i] would yield (107, 175, 5638)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2305 635355 887606 329663 022614 151478 962001 999420 137033 605569 491413 825367 514938 492277 122226 535040 466815 436960 > 4¹⁷⁵ [i]