MinT - Best Known (129, 224, s)-Nets in Base 4

Best Known (129, 224, s)-Nets in Base 4

(129, 224, 130)-Net over F₄ — Constructive and digital

Digital (129, 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]

(129, 224, 268)-Net over F₄ — Digital

Digital (129, 224, 268)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 224, 4362)-Net in Base 4 — Upper bound on s

There is no (129, 224, 4363)-net in base 4, because

1 times m-reduction [i] would yield (129, 223, 4363)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 182 573291 604603 032051 374819 200257 721325 702726 533773 583087 249631 131689 693989 642013 142393 146101 830480 877812 244472 174315 588720 602547 865088 > 4²²³ [i]