MinT - Best Known (225−101, 225, s)-Nets in Base 4

Best Known (225−101, 225, s)-Nets in Base 4

(225−101, 225, 130)-Net over F₄ — Constructive and digital

Digital (124, 225, 130)-net over F₄, using

t-expansion [i] based on digital (105, 225, 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]

(225−101, 225, 224)-Net over F₄ — Digital

Digital (124, 225, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−101, 225, 3193)-Net in Base 4 — Upper bound on s

There is no (124, 225, 3194)-net in base 4, because

1 times m-reduction [i] would yield (124, 224, 3194)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 735 333403 638695 995307 274147 831022 329225 371433 195704 653426 713935 991315 114677 550595 158888 474771 732359 988689 817975 957252 418429 289716 487308 > 4²²⁴ [i]