MinT - Best Known (86, 86+37, s)-Nets in Base 4

Best Known (86, 86+37, s)-Nets in Base 4

(86, 86+37, 312)-Net over F₄ — Constructive and digital

Digital (86, 123, 312)-net over F₄, using

t-expansion [i] based on digital (85, 123, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 41, 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]

(86, 86+37, 557)-Net over F₄ — Digital

Digital (86, 123, 557)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+37, 30299)-Net in Base 4 — Upper bound on s

There is no (86, 123, 30300)-net in base 4, because

1 times m-reduction [i] would yield (86, 122, 30300)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 284482 853208 593456 487948 024230 331274 684220 885829 601331 734402 376462 245941 > 4¹²² [i]