MinT - Best Known (234−112, 234, s)-Nets in Base 4

Best Known (234−112, 234, s)-Nets in Base 4

(234−112, 234, 130)-Net over F₄ — Constructive and digital

Digital (122, 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]

(234−112, 234, 189)-Net over F₄ — Digital

Digital (122, 234, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−112, 234, 2327)-Net in Base 4 — Upper bound on s

There is no (122, 234, 2328)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 779 952257 065672 993313 040318 116812 649620 498158 496836 603439 211380 933013 161884 146234 852976 489525 238899 146700 563822 160410 587064 861082 673728 320800 > 4²³⁴ [i]