MinT - Best Known (221−113, 221, s)-Nets in Base 4

Best Known (221−113, 221, s)-Nets in Base 4

(221−113, 221, 130)-Net over F₄ — Constructive and digital

Digital (108, 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]

(221−113, 221, 146)-Net over F₄ — Digital

Digital (108, 221, 146)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−113, 221, 1632)-Net in Base 4 — Upper bound on s

There is no (108, 221, 1633)-net in base 4, because

1 times m-reduction [i] would yield (108, 220, 1633)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 919066 667249 357619 316126 554323 761633 624751 820795 332907 871441 074402 279484 463373 599882 317164 581657 750905 239893 254975 694677 517490 571880 > 4²²⁰ [i]