MinT - Best Known (144, 213, s)-Nets in Base 4

Best Known (144, 213, s)-Nets in Base 4

(144, 213, 240)-Net over F₄ — Constructive and digital

Digital (144, 213, 240)-net over F₄, using

t-expansion [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, 213, 646)-Net over F₄ — Digital

Digital (144, 213, 646)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 213, 25580)-Net in Base 4 — Upper bound on s

There is no (144, 213, 25581)-net in base 4, because

1 times m-reduction [i] would yield (144, 212, 25581)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 371490 569190 236780 556993 813913 657770 308038 944465 505144 692595 709482 214285 922686 645945 873219 409981 349720 225964 946224 226856 947006 > 4²¹² [i]