MinT - Best Known (142, 142+66, s)-Nets in Base 4

Best Known (142, 142+66, s)-Nets in Base 4

(142, 142+66, 312)-Net over F₄ — Constructive and digital

Digital (142, 208, 312)-net over F₄, using

4¹ times duplication [i] based on digital (141, 207, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 69, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(142, 142+66, 685)-Net over F₄ — Digital

Digital (142, 208, 685)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+66, 27327)-Net in Base 4 — Upper bound on s

There is no (142, 208, 27328)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169247 432714 585961 164816 443385 719384 986386 676900 263530 795868 679888 301336 173914 247778 806053 521161 994690 300436 906018 287745 415655 > 4²⁰⁸ [i]