MinT - Best Known (188−79, 188, s)-Nets in Base 4

Best Known (188−79, 188, s)-Nets in Base 4

(188−79, 188, 130)-Net over F₄ — Constructive and digital

Digital (109, 188, 130)-net over F₄, using

t-expansion [i] based on digital (105, 188, 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]

(188−79, 188, 236)-Net over F₄ — Digital

Digital (109, 188, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−79, 188, 3922)-Net in Base 4 — Upper bound on s

There is no (109, 188, 3923)-net in base 4, because

1 times m-reduction [i] would yield (109, 187, 3923)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38586 333999 471034 058330 464391 405457 041667 738777 073809 464839 251520 350306 032636 304749 718190 194821 105349 614870 454592 > 4¹⁸⁷ [i]