MinT - Best Known (114, 250, s)-Nets in Base 4

Best Known (114, 250, s)-Nets in Base 4

(114, 250, 130)-Net over F₄ — Constructive and digital

Digital (114, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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, 250, 165)-Net over F₄ — Digital

Digital (114, 250, 165)-net over F₄, using

t-expansion [i] based on digital (109, 250, 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, 250, 1369)-Net in Base 4 — Upper bound on s

There is no (114, 250, 1370)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 282607 229730 741085 920862 143827 786400 512041 290499 345546 676266 946885 509767 100218 641378 456089 438870 306527 538865 299394 027304 745838 348941 303747 285655 866282 > 4²⁵⁰ [i]