MinT - Best Known (134, 253, s)-Nets in Base 4

Best Known (134, 253, s)-Nets in Base 4

(134, 253, 130)-Net over F₄ — Constructive and digital

Digital (134, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(134, 253, 215)-Net over F₄ — Digital

Digital (134, 253, 215)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 253, 2787)-Net in Base 4 — Upper bound on s

There is no (134, 253, 2788)-net in base 4, because

1 times m-reduction [i] would yield (134, 252, 2788)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 597283 985975 376654 692007 112451 109063 981373 590918 594549 545726 734823 731746 596098 784708 725363 674551 639814 288385 775564 750099 154783 235919 543616 283060 971720 > 4²⁵² [i]