MinT - Best Known (113−53, 113, s)-Nets in Base 4

Best Known (113−53, 113, s)-Nets in Base 4

(113−53, 113, 76)-Net over F₄ — Constructive and digital

Digital (60, 113, 76)-net over F₄, using

1 times m-reduction [i] based on digital (60, 114, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 57, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(113−53, 113, 109)-Net over F₄ — Digital

Digital (60, 113, 109)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−53, 113, 1358)-Net in Base 4 — Upper bound on s

There is no (60, 113, 1359)-net in base 4, because

1 times m-reduction [i] would yield (60, 112, 1359)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 336225 394500 544960 021013 435773 880653 992463 288490 757314 340661 557988 > 4¹¹² [i]