MinT - Best Known (117, 117+111, s)-Nets in Base 4

Best Known (117, 117+111, s)-Nets in Base 4

(117, 117+111, 130)-Net over F₄ — Constructive and digital

Digital (117, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(117, 117+111, 175)-Net over F₄ — Digital

Digital (117, 228, 175)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+111, 2127)-Net in Base 4 — Upper bound on s

There is no (117, 228, 2128)-net in base 4, because

1 times m-reduction [i] would yield (117, 227, 2128)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47424 810687 709640 282326 791612 155247 436323 656851 230808 258402 272219 830965 268053 791126 343022 364343 103547 815617 600331 542418 382412 071824 893444 > 4²²⁷ [i]