MinT - Best Known (256−119, 256, s)-Nets in Base 4

Best Known (256−119, 256, s)-Nets in Base 4

(256−119, 256, 130)-Net over F₄ — Constructive and digital

Digital (137, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(256−119, 256, 225)-Net over F₄ — Digital

Digital (137, 256, 225)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−119, 256, 2994)-Net in Base 4 — Upper bound on s

There is no (137, 256, 2995)-net in base 4, because

1 times m-reduction [i] would yield (137, 255, 2995)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3357 959205 999448 489134 340865 289445 036895 365656 671278 887526 129661 819804 458144 142987 752237 984451 513263 456237 978562 384958 774929 936891 203620 089385 364352 874688 > 4²⁵⁵ [i]