MinT - Best Known (120, 120+119, s)-Nets in Base 4

Best Known (120, 120+119, s)-Nets in Base 4

(120, 120+119, 130)-Net over F₄ — Constructive and digital

Digital (120, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(120, 120+119, 171)-Net over F₄ — Digital

Digital (120, 239, 171)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+119, 1992)-Net in Base 4 — Upper bound on s

There is no (120, 239, 1993)-net in base 4, because

1 times m-reduction [i] would yield (120, 238, 1993)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195766 871957 355615 912174 128968 759135 666122 481913 191500 258483 719994 045005 570992 330327 011415 179889 158876 530923 165582 799115 946496 902389 450471 531328 > 4²³⁸ [i]