MinT - Best Known (226−103, 226, s)-Nets in Base 4

Best Known (226−103, 226, s)-Nets in Base 4

(226−103, 226, 130)-Net over F₄ — Constructive and digital

Digital (123, 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]

(226−103, 226, 214)-Net over F₄ — Digital

Digital (123, 226, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−103, 226, 2956)-Net in Base 4 — Upper bound on s

There is no (123, 226, 2957)-net in base 4, because

1 times m-reduction [i] would yield (123, 225, 2957)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2928 793331 497072 103022 143869 967796 635551 263713 191620 464255 487679 542319 713239 707992 146795 488105 870973 820958 030019 079750 630200 273140 735840 > 4²²⁵ [i]