MinT - Best Known (251−117, 251, s)-Nets in Base 4

Best Known (251−117, 251, s)-Nets in Base 4

(251−117, 251, 130)-Net over F₄ — Constructive and digital

Digital (134, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 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]

(251−117, 251, 219)-Net over F₄ — Digital

Digital (134, 251, 219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−117, 251, 2898)-Net in Base 4 — Upper bound on s

There is no (134, 251, 2899)-net in base 4, because

1 times m-reduction [i] would yield (134, 250, 2899)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 326356 124318 848570 820772 210884 591416 997249 693731 814763 382402 141179 250334 656331 033479 274587 054761 048798 552277 643323 871900 266291 839923 428673 840966 826472 > 4²⁵⁰ [i]