MinT - Best Known (143−45, 143, s)-Nets in Base 4

Best Known (143−45, 143, s)-Nets in Base 4

(143−45, 143, 240)-Net over F₄ — Constructive and digital

Digital (98, 143, 240)-net over F₄, using

t-expansion [i] based on digital (97, 143, 240)-net over F₄, using
- 1 times m-reduction [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]

(143−45, 143, 518)-Net over F₄ — Digital

Digital (98, 143, 518)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−45, 143, 23196)-Net in Base 4 — Upper bound on s

There is no (98, 143, 23197)-net in base 4, because

1 times m-reduction [i] would yield (98, 142, 23197)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 098638 570527 378165 918258 152565 532780 760529 238690 221699 746666 172158 226617 225966 818260 > 4¹⁴² [i]