MinT - Best Known (114, 114+123, s)-Nets in Base 4

Best Known (114, 114+123, s)-Nets in Base 4

(114, 114+123, 130)-Net over F₄ — Constructive and digital

Digital (114, 237, 130)-net over F₄, using

t-expansion [i] based on digital (105, 237, 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+123, 165)-Net over F₄ — Digital

Digital (114, 237, 165)-net over F₄, using

t-expansion [i] based on digital (109, 237, 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+123, 1626)-Net in Base 4 — Upper bound on s

There is no (114, 237, 1627)-net in base 4, because

1 times m-reduction [i] would yield (114, 236, 1627)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12350 849360 230906 108416 985414 620198 673299 052190 365832 959982 056797 649370 627728 117815 560565 369093 829868 867240 071386 980509 873500 321915 881905 581472 > 4²³⁶ [i]