MinT - Best Known (208−57, 208, s)-Nets in Base 4

Best Known (208−57, 208, s)-Nets in Base 4

(208−57, 208, 531)-Net over F₄ — Constructive and digital

Digital (151, 208, 531)-net over F₄, using

8 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 72, 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]

(208−57, 208, 1271)-Net over F₄ — Digital

Digital (151, 208, 1271)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−57, 208, 106349)-Net in Base 4 — Upper bound on s

There is no (151, 208, 106350)-net in base 4, because

1 times m-reduction [i] would yield (151, 207, 106350)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42316 959526 335022 375260 696005 174839 161078 506445 113257 879760 758596 068287 159588 131510 980442 963060 031925 647765 013548 462587 680998 > 4²⁰⁷ [i]