MinT - Best Known (212−68, 212, s)-Nets in Base 4

Best Known (212−68, 212, s)-Nets in Base 4

(212−68, 212, 240)-Net over F₄ — Constructive and digital

Digital (144, 212, 240)-net over F₄, using

t-expansion [i] based on digital (143, 212, 240)-net over F₄, using
- 1 times m-reduction [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]

(212−68, 212, 668)-Net over F₄ — Digital

Digital (144, 212, 668)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−68, 212, 25580)-Net in Base 4 — Upper bound on s

There is no (144, 212, 25581)-net in base 4, because

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]