MinT - Best Known (123, 216, s)-Nets in Base 4

Best Known (123, 216, s)-Nets in Base 4

(123, 216, 130)-Net over F₄ — Constructive and digital

Digital (123, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 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]

(123, 216, 247)-Net over F₄ — Digital

Digital (123, 216, 247)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 216, 3871)-Net in Base 4 — Upper bound on s

There is no (123, 216, 3872)-net in base 4, because

1 times m-reduction [i] would yield (123, 215, 3872)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2789 810197 965649 441306 252125 707012 298372 070892 446644 268989 127964 227345 496263 929080 138930 622293 085920 341903 231882 399741 105888 275352 > 4²¹⁵ [i]