MinT - Best Known (145−47, 145, s)-Nets in Base 4

Best Known (145−47, 145, s)-Nets in Base 4

(145−47, 145, 240)-Net over F₄ — Constructive and digital

Digital (98, 145, 240)-net over F₄, using

4¹ times duplication [i] based on digital (97, 144, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 48, 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]

(145−47, 145, 466)-Net over F₄ — Digital

Digital (98, 145, 466)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−47, 145, 18463)-Net in Base 4 — Upper bound on s

There is no (98, 145, 18464)-net in base 4, because

1 times m-reduction [i] would yield (98, 144, 18464)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 596156 002374 383976 975407 189620 365730 807039 267919 593788 489149 217293 745541 749799 767467 > 4¹⁴⁴ [i]