MinT - Best Known (214−59, 214, s)-Nets in Base 4

Best Known (214−59, 214, s)-Nets in Base 4

(214−59, 214, 531)-Net over F₄ — Constructive and digital

Digital (155, 214, 531)-net over F₄, using

8 times m-reduction [i] based on digital (155, 222, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 74, 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]

(214−59, 214, 1266)-Net over F₄ — Digital

Digital (155, 214, 1266)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−59, 214, 102784)-Net in Base 4 — Upper bound on s

There is no (155, 214, 102785)-net in base 4, because

1 times m-reduction [i] would yield (155, 213, 102785)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 316291 141328 586350 826544 067264 796973 413816 216389 319773 230884 945283 296580 002453 324198 907695 798019 592840 745661 639568 575029 151232 > 4²¹³ [i]