MinT - Best Known (114, 114+118, s)-Nets in Base 4

Best Known (114, 114+118, s)-Nets in Base 4

(114, 114+118, 130)-Net over F₄ — Constructive and digital

Digital (114, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(114, 114+118, 165)-Net over F₄ — Digital

Digital (114, 232, 165)-net over F₄, using

t-expansion [i] based on digital (109, 232, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(114, 114+118, 1724)-Net in Base 4 — Upper bound on s

There is no (114, 232, 1725)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 340204 989507 335187 910112 166875 514081 042712 538388 270518 378503 644510 891991 380242 633303 445927 992687 327701 784801 769641 327115 818826 655199 520700 > 4²³² [i]