MinT - Best Known (81, 81+33, s)-Nets in Base 4

Best Known (81, 81+33, s)-Nets in Base 4

(81, 81+33, 384)-Net over F₄ — Constructive and digital

Digital (81, 114, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 38, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(81, 81+33, 611)-Net over F₄ — Digital

Digital (81, 114, 611)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+33, 40488)-Net in Base 4 — Upper bound on s

There is no (81, 114, 40489)-net in base 4, because

1 times m-reduction [i] would yield (81, 113, 40489)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 107 873588 445762 142257 788589 593291 348537 343606 585377 823098 917255 597810 > 4¹¹³ [i]