MinT - Best Known (127, 248, s)-Nets in Base 4

Best Known (127, 248, s)-Nets in Base 4

(127, 248, 130)-Net over F₄ — Constructive and digital

Digital (127, 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]

(127, 248, 188)-Net over F₄ — Digital

Digital (127, 248, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 248, 2277)-Net in Base 4 — Upper bound on s

There is no (127, 248, 2278)-net in base 4, because

1 times m-reduction [i] would yield (127, 247, 2278)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52002 800403 788125 732398 742497 137803 121910 835939 292932 357966 186326 065063 104005 052444 116978 106259 716506 477619 007939 973406 028442 095455 759472 025629 815720 > 4²⁴⁷ [i]