MinT - Best Known (224−109, 224, s)-Nets in Base 4

Best Known (224−109, 224, s)-Nets in Base 4

(224−109, 224, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(224−109, 224, 173)-Net over F₄ — Digital

Digital (115, 224, 173)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−109, 224, 2097)-Net in Base 4 — Upper bound on s

There is no (115, 224, 2098)-net in base 4, because

1 times m-reduction [i] would yield (115, 223, 2098)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 184 980842 030353 444273 766327 837376 755305 310801 441075 763590 257344 977731 751147 590820 248874 859481 744342 559932 697549 044316 874793 998061 818880 > 4²²³ [i]