MinT - Best Known (234−122, 234, s)-Nets in Base 4

Best Known (234−122, 234, s)-Nets in Base 4

(234−122, 234, 130)-Net over F₄ — Constructive and digital

Digital (112, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−122, 234, 165)-Net over F₄ — Digital

Digital (112, 234, 165)-net over F₄, using

t-expansion [i] based on digital (109, 234, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(234−122, 234, 1552)-Net in Base 4 — Upper bound on s

There is no (112, 234, 1553)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 786 188716 401274 475099 667052 487549 913575 405967 460851 720889 066439 557466 168946 831709 371915 641986 805932 215544 526551 600043 917167 155655 927232 000000 > 4²³⁴ [i]