MinT - Best Known (123, 246, s)-Nets in Base 4

Best Known (123, 246, s)-Nets in Base 4

(123, 246, 130)-Net over F₄ — Constructive and digital

Digital (123, 246, 130)-net over F₄, using

t-expansion [i] based on digital (105, 246, 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, 246, 173)-Net over F₄ — Digital

Digital (123, 246, 173)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 246, 2007)-Net in Base 4 — Upper bound on s

There is no (123, 246, 2008)-net in base 4, because

1 times m-reduction [i] would yield (123, 245, 2008)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3291 335862 757817 852424 661706 714800 126399 315080 180801 704185 029755 722715 327756 517676 473747 176127 381132 752708 479347 999042 203049 221946 486689 649745 460920 > 4²⁴⁵ [i]