MinT - Best Known (56, 56+51, s)-Nets in Base 4

Best Known (56, 56+51, s)-Nets in Base 4

(56, 56+51, 66)-Net over F₄ — Constructive and digital

Digital (56, 107, 66)-net over F₄, using

t-expansion [i] based on digital (49, 107, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(56, 56+51, 99)-Net over F₄ — Digital

Digital (56, 107, 99)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+51, 1191)-Net in Base 4 — Upper bound on s

There is no (56, 107, 1192)-net in base 4, because

1 times m-reduction [i] would yield (56, 106, 1192)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6710 731379 147297 780791 603480 798532 521576 631055 291596 979752 728420 > 4¹⁰⁶ [i]