MinT - Best Known (139−65, 139, s)-Nets in Base 4

Best Known (139−65, 139, s)-Nets in Base 4

(139−65, 139, 104)-Net over F₄ — Constructive and digital

Digital (74, 139, 104)-net over F₄, using

t-expansion [i] based on digital (73, 139, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(139−65, 139, 130)-Net over F₄ — Digital

Digital (74, 139, 130)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−65, 139, 1657)-Net in Base 4 — Upper bound on s

There is no (74, 139, 1658)-net in base 4, because

1 times m-reduction [i] would yield (74, 138, 1658)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 123240 081474 300045 144010 342633 252960 477482 096134 364052 463049 849630 758214 270119 392717 > 4¹³⁸ [i]