MinT - Best Known (256−117, 256, s)-Nets in Base 4

Best Known (256−117, 256, s)-Nets in Base 4

(256−117, 256, 130)-Net over F₄ — Constructive and digital

Digital (139, 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]

(256−117, 256, 238)-Net over F₄ — Digital

Digital (139, 256, 238)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−117, 256, 3272)-Net in Base 4 — Upper bound on s

There is no (139, 256, 3273)-net in base 4, because

1 times m-reduction [i] would yield (139, 255, 3273)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3405 720120 931843 800051 804342 995525 286545 030079 083466 750501 753641 751003 262061 916754 362354 373175 994906 774468 249296 272614 328866 396334 990124 160193 190040 794080 > 4²⁵⁵ [i]