MinT - Best Known (224−123, 224, s)-Nets in Base 4

Best Known (224−123, 224, s)-Nets in Base 4

(224−123, 224, 104)-Net over F₄ — Constructive and digital

Digital (101, 224, 104)-net over F₄, using

t-expansion [i] based on digital (73, 224, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(224−123, 224, 144)-Net over F₄ — Digital

Digital (101, 224, 144)-net over F₄, using

t-expansion [i] based on digital (91, 224, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(224−123, 224, 1198)-Net in Base 4 — Upper bound on s

There is no (101, 224, 1199)-net in base 4, because

1 times m-reduction [i] would yield (101, 223, 1199)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 620047 386903 857704 612543 235484 378407 613790 772884 939172 653920 968375 335691 971515 897791 997243 026731 556105 088414 960452 490553 421143 523664 > 4²²³ [i]