MinT - Best Known (129, 250, s)-Nets in Base 4

Best Known (129, 250, s)-Nets in Base 4

(129, 250, 130)-Net over F₄ — Constructive and digital

Digital (129, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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]

(129, 250, 194)-Net over F₄ — Digital

Digital (129, 250, 194)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 250, 2387)-Net in Base 4 — Upper bound on s

There is no (129, 250, 2388)-net in base 4, because

1 times m-reduction [i] would yield (129, 249, 2388)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 831215 932859 263550 511398 506928 013468 760780 901514 674855 597186 347956 861603 072892 621556 375335 229387 049045 049110 787889 743612 092922 197806 893125 982331 367568 > 4²⁴⁹ [i]