MinT - Best Known (252−144, 252, s)-Nets in Base 4

Best Known (252−144, 252, s)-Nets in Base 4

(252−144, 252, 130)-Net over F₄ — Constructive and digital

Digital (108, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(252−144, 252, 144)-Net over F₄ — Digital

Digital (108, 252, 144)-net over F₄, using

t-expansion [i] based on digital (91, 252, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(252−144, 252, 1120)-Net in Base 4 — Upper bound on s

There is no (108, 252, 1121)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53 077466 753209 625166 420042 590329 515495 591239 646532 696754 685195 389375 364442 581512 368081 693216 755882 902650 130558 893241 558838 481878 649705 407449 641812 861316 > 4²⁵² [i]