MinT - Best Known (91, 91+34, s)-Nets in Base 4

Best Known (91, 91+34, s)-Nets in Base 4

(91, 91+34, 531)-Net over F₄ — Constructive and digital

Digital (91, 125, 531)-net over F₄, using

1 times m-reduction [i] based on digital (91, 126, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 42, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(91, 91+34, 853)-Net over F₄ — Digital

Digital (91, 125, 853)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+34, 63920)-Net in Base 4 — Upper bound on s

There is no (91, 125, 63921)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1809 304126 158820 563741 535230 534402 749566 216709 101877 624734 448029 010434 961596 > 4¹²⁵ [i]