MinT - Best Known (105−31, 105, s)-Nets in Base 4

Best Known (105−31, 105, s)-Nets in Base 4

(105−31, 105, 312)-Net over F₄ — Constructive and digital

Digital (74, 105, 312)-net over F₄, using

t-expansion [i] based on digital (73, 105, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 35, 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]

(105−31, 105, 529)-Net over F₄ — Digital

Digital (74, 105, 529)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−31, 105, 31971)-Net in Base 4 — Upper bound on s

There is no (74, 105, 31972)-net in base 4, because

1 times m-reduction [i] would yield (74, 104, 31972)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 411 443783 288441 266774 691973 988319 968365 117648 995144 873555 599096 > 4¹⁰⁴ [i]