MinT - Best Known (117, 117+85, s)-Nets in Base 4

Best Known (117, 117+85, s)-Nets in Base 4

(117, 117+85, 130)-Net over F₄ — Constructive and digital

Digital (117, 202, 130)-net over F₄, using

t-expansion [i] based on digital (105, 202, 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+85, 251)-Net over F₄ — Digital

Digital (117, 202, 251)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+85, 4153)-Net in Base 4 — Upper bound on s

There is no (117, 202, 4154)-net in base 4, because

1 times m-reduction [i] would yield (117, 201, 4154)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 408787 620333 683274 440250 130645 991727 830016 913515 954161 621742 198608 305493 156836 351673 050802 958983 714612 444693 395140 910320 > 4²⁰¹ [i]