MinT - Best Known (221−93, 221, s)-Nets in Base 4

Best Known (221−93, 221, s)-Nets in Base 4

(221−93, 221, 130)-Net over F₄ — Constructive and digital

Digital (128, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 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]

(221−93, 221, 271)-Net over F₄ — Digital

Digital (128, 221, 271)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−93, 221, 4507)-Net in Base 4 — Upper bound on s

There is no (128, 221, 4508)-net in base 4, because

1 times m-reduction [i] would yield (128, 220, 4508)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 862212 560426 580677 651772 331146 565296 992768 493866 149655 669552 833625 997781 936820 585086 476905 904292 102373 641714 484897 844683 967407 221040 > 4²²⁰ [i]