MinT - Best Known (186−79, 186, s)-Nets in Base 4

Best Known (186−79, 186, s)-Nets in Base 4

(186−79, 186, 130)-Net over F₄ — Constructive and digital

Digital (107, 186, 130)-net over F₄, using

t-expansion [i] based on digital (105, 186, 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]

(186−79, 186, 226)-Net over F₄ — Digital

Digital (107, 186, 226)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−79, 186, 3651)-Net in Base 4 — Upper bound on s

There is no (107, 186, 3652)-net in base 4, because

1 times m-reduction [i] would yield (107, 185, 3652)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2421 705386 285885 999556 047247 849606 974062 985563 826486 657714 302682 631358 596608 335397 789356 548613 993866 177019 279888 > 4¹⁸⁵ [i]