MinT - Best Known (226−105, 226, s)-Nets in Base 4

Best Known (226−105, 226, s)-Nets in Base 4

(226−105, 226, 130)-Net over F₄ — Constructive and digital

Digital (121, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 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]

(226−105, 226, 202)-Net over F₄ — Digital

Digital (121, 226, 202)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−105, 226, 2672)-Net in Base 4 — Upper bound on s

There is no (121, 226, 2673)-net in base 4, because

1 times m-reduction [i] would yield (121, 225, 2673)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2913 985622 542184 718828 068199 996499 325757 964312 194388 003276 240282 745259 930598 429105 632067 126680 616397 483335 937616 258950 028338 255609 203600 > 4²²⁵ [i]