MinT - Best Known (224−99, 224, s)-Nets in Base 4

Best Known (224−99, 224, s)-Nets in Base 4

(224−99, 224, 130)-Net over F₄ — Constructive and digital

Digital (125, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 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]

(224−99, 224, 234)-Net over F₄ — Digital

Digital (125, 224, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−99, 224, 3460)-Net in Base 4 — Upper bound on s

There is no (125, 224, 3461)-net in base 4, because

1 times m-reduction [i] would yield (125, 223, 3461)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 182 474349 766398 657561 946835 967426 382374 352083 884993 124009 380158 327757 322588 825300 323707 620451 444060 384032 085449 914136 303805 502758 908928 > 4²²³ [i]