MinT - Best Known (111−56, 111, s)-Nets in Base 4

Best Known (111−56, 111, s)-Nets in Base 4

(111−56, 111, 66)-Net over F₄ — Constructive and digital

Digital (55, 111, 66)-net over F₄, using

t-expansion [i] based on digital (49, 111, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(111−56, 111, 91)-Net over F₄ — Digital

Digital (55, 111, 91)-net over F₄, using

t-expansion [i] based on digital (50, 111, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(111−56, 111, 894)-Net in Base 4 — Upper bound on s

There is no (55, 111, 895)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 757432 765573 333590 132358 040565 898936 767338 547811 795034 324451 302869 > 4¹¹¹ [i]