MinT - Best Known (224−117, 224, s)-Nets in Base 4

Best Known (224−117, 224, s)-Nets in Base 4

(224−117, 224, 130)-Net over F₄ — Constructive and digital

Digital (107, 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]

(224−117, 224, 144)-Net over F₄ — Digital

Digital (107, 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]

(224−117, 224, 1497)-Net in Base 4 — Upper bound on s

There is no (107, 224, 1498)-net in base 4, because

1 times m-reduction [i] would yield (107, 223, 1498)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 183 747375 635450 982356 505355 150675 271544 576054 551159 173804 854390 051993 170819 645462 024814 781528 378224 998228 557802 522601 040483 903121 009680 > 4²²³ [i]