MinT - Best Known (144, 214, s)-Nets in Base 4

Best Known (144, 214, s)-Nets in Base 4

(144, 214, 240)-Net over F₄ — Constructive and digital

Digital (144, 214, 240)-net over F₄, using

4¹ times duplication [i] based on digital (143, 213, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 71, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(144, 214, 626)-Net over F₄ — Digital

Digital (144, 214, 626)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 214, 22220)-Net in Base 4 — Upper bound on s

There is no (144, 214, 22221)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 943963 571705 134001 730488 293522 620683 097867 397085 966498 344371 555454 290253 360500 889532 591614 649397 015232 932563 602761 750326 092408 > 4²¹⁴ [i]