MinT - Best Known (231−101, 231, s)-Nets in Base 4

Best Known (231−101, 231, s)-Nets in Base 4

(231−101, 231, 130)-Net over F₄ — Constructive and digital

Digital (130, 231, 130)-net over F₄, using

t-expansion [i] based on digital (105, 231, 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]

(231−101, 231, 249)-Net over F₄ — Digital

Digital (130, 231, 249)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−101, 231, 3778)-Net in Base 4 — Upper bound on s

There is no (130, 231, 3779)-net in base 4, because

1 times m-reduction [i] would yield (130, 230, 3779)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 993256 222503 921601 690445 406742 923655 479960 969707 208623 444420 556131 424966 347926 602808 522585 209212 357577 694765 480699 486990 457081 676206 203940 > 4²³⁰ [i]