MinT - Best Known (230−45, 230, s)-Nets in Base 4

Best Known (230−45, 230, s)-Nets in Base 4

(230−45, 230, 1539)-Net over F₄ — Constructive and digital

Digital (185, 230, 1539)-net over F₄, using

t-expansion [i] based on digital (184, 230, 1539)-net over F₄, using
- 4 times m-reduction [i] based on digital (184, 234, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 78, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(230−45, 230, 8093)-Net over F₄ — Digital

Digital (185, 230, 8093)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−45, 230, 5579914)-Net in Base 4 — Upper bound on s

There is no (185, 230, 5579915)-net in base 4, because

1 times m-reduction [i] would yield (185, 229, 5579915)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744283 480199 685264 754736 277071 713641 089821 475690 477062 230410 044766 995409 076105 466935 699101 931434 195647 943127 563796 851875 504587 129778 218736 > 4²²⁹ [i]