MinT - Best Known (138, 253, s)-Nets in Base 4

Best Known (138, 253, s)-Nets in Base 4

(138, 253, 130)-Net over F₄ — Constructive and digital

Digital (138, 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]

(138, 253, 239)-Net over F₄ — Digital

Digital (138, 253, 239)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 253, 3330)-Net in Base 4 — Upper bound on s

There is no (138, 253, 3331)-net in base 4, because

1 times m-reduction [i] would yield (138, 252, 3331)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 474561 550575 811398 463613 527496 618413 182057 484360 415551 003797 992474 354647 092981 522130 281665 064143 708802 657350 664415 539586 463990 704840 948891 923694 562880 > 4²⁵² [i]