MinT - Best Known (155−47, 155, s)-Nets in Base 4

Best Known (155−47, 155, s)-Nets in Base 4

(155−47, 155, 312)-Net over F₄ — Constructive and digital

Digital (108, 155, 312)-net over F₄, using

t-expansion [i] based on digital (107, 155, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (107, 156, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 52, 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]

(155−47, 155, 644)-Net over F₄ — Digital

Digital (108, 155, 644)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−47, 155, 33750)-Net in Base 4 — Upper bound on s

There is no (108, 155, 33751)-net in base 4, because

1 times m-reduction [i] would yield (108, 154, 33751)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 685842 295391 357460 762556 558278 338992 181846 440323 336541 543278 289556 700478 172340 125395 377164 > 4¹⁵⁴ [i]