MinT - Best Known (254−144, 254, s)-Nets in Base 4

Best Known (254−144, 254, s)-Nets in Base 4

(254−144, 254, 130)-Net over F₄ — Constructive and digital

Digital (110, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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]

(254−144, 254, 165)-Net over F₄ — Digital

Digital (110, 254, 165)-net over F₄, using

t-expansion [i] based on digital (109, 254, 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]

(254−144, 254, 1167)-Net in Base 4 — Upper bound on s

There is no (110, 254, 1168)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 886 959985 012211 226594 432199 732447 018917 312994 287021 128361 128079 636805 166954 903947 177920 457518 014230 077881 285409 472478 371610 922136 630788 623494 866619 076530 > 4²⁵⁴ [i]