MinT - Best Known (114, 114+47, s)-Nets in Base 4

Best Known (114, 114+47, s)-Nets in Base 4

(114, 114+47, 384)-Net over F₄ — Constructive and digital

Digital (114, 161, 384)-net over F₄, using

t-expansion [i] based on digital (113, 161, 384)-net over F₄, using
- 1 times m-reduction [i] based on digital (113, 162, 384)-net over F₄, using
  - trace code for nets [i] based on digital (5, 54, 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]

(114, 114+47, 780)-Net over F₄ — Digital

Digital (114, 161, 780)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+47, 48463)-Net in Base 4 — Upper bound on s

There is no (114, 161, 48464)-net in base 4, because

1 times m-reduction [i] would yield (114, 160, 48464)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 136895 762660 306600 322701 143620 599110 322496 849346 070469 279069 619328 053344 213855 251073 415022 493092 > 4¹⁶⁰ [i]