MinT - Best Known (212−103, 212, s)-Nets in Base 4

Best Known (212−103, 212, s)-Nets in Base 4

(212−103, 212, 130)-Net over F₄ — Constructive and digital

Digital (109, 212, 130)-net over F₄, using

t-expansion [i] based on digital (105, 212, 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]

(212−103, 212, 166)-Net over F₄ — Digital

Digital (109, 212, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−103, 212, 2007)-Net in Base 4 — Upper bound on s

There is no (109, 212, 2008)-net in base 4, because

1 times m-reduction [i] would yield (109, 211, 2008)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 926130 220584 740370 905138 092013 615862 923516 579560 042162 304191 377243 455712 714901 711928 495404 769871 673564 303222 403962 571251 123950 > 4²¹¹ [i]