MinT - Best Known (111, 188, s)-Nets in Base 4

Best Known (111, 188, s)-Nets in Base 4

(111, 188, 130)-Net over F₄ — Constructive and digital

Digital (111, 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]

(111, 188, 256)-Net over F₄ — Digital

Digital (111, 188, 256)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 188, 4565)-Net in Base 4 — Upper bound on s

There is no (111, 188, 4566)-net in base 4, because

1 times m-reduction [i] would yield (111, 187, 4566)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38585 735774 104926 519457 988784 174085 752954 106961 956054 435885 360694 708179 276402 159648 803550 773829 081710 342887 384320 > 4¹⁸⁷ [i]