MinT - Best Known (131, 131+117, s)-Nets in Base 4

Best Known (131, 131+117, s)-Nets in Base 4

(131, 131+117, 130)-Net over F₄ — Constructive and digital

Digital (131, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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]

(131, 131+117, 209)-Net over F₄ — Digital

Digital (131, 248, 209)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+117, 2694)-Net in Base 4 — Upper bound on s

There is no (131, 248, 2695)-net in base 4, because

1 times m-reduction [i] would yield (131, 247, 2695)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51823 342942 565077 099696 474226 863736 172483 929122 878060 651052 714039 205282 585962 009785 647931 743991 180287 783742 400370 189291 350051 486237 064452 822115 709904 > 4²⁴⁷ [i]