MinT - Best Known (117, 117+89, s)-Nets in Base 4

Best Known (117, 117+89, s)-Nets in Base 4

(117, 117+89, 130)-Net over F₄ — Constructive and digital

Digital (117, 206, 130)-net over F₄, using

t-expansion [i] based on digital (105, 206, 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]

(117, 117+89, 234)-Net over F₄ — Digital

Digital (117, 206, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+89, 3635)-Net in Base 4 — Upper bound on s

There is no (117, 206, 3636)-net in base 4, because

1 times m-reduction [i] would yield (117, 205, 3636)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2658 363827 248855 504458 870575 240269 532302 763349 391050 044533 624970 263248 765526 495043 656754 428958 192206 661043 271506 937586 809180 > 4²⁰⁵ [i]