MinT - Best Known (136, 136+111, s)-Nets in Base 4

Best Known (136, 136+111, s)-Nets in Base 4

(136, 136+111, 130)-Net over F₄ — Constructive and digital

Digital (136, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(136, 136+111, 242)-Net over F₄ — Digital

Digital (136, 247, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+111, 3461)-Net in Base 4 — Upper bound on s

There is no (136, 247, 3462)-net in base 4, because

1 times m-reduction [i] would yield (136, 246, 3462)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12888 723831 326615 508303 120335 810437 794292 763218 441762 211685 658843 132179 837648 488076 552584 122345 850589 646286 157061 814685 914948 083376 050285 104792 623680 > 4²⁴⁶ [i]