MinT - Best Known (230−47, 230, s)-Nets in Base 4

Best Known (230−47, 230, s)-Nets in Base 4

(230−47, 230, 1539)-Net over F₄ — Constructive and digital

Digital (183, 230, 1539)-net over F₄, using

t-expansion [i] based on digital (182, 230, 1539)-net over F₄, using
- 1 times m-reduction [i] based on digital (182, 231, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 77, 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]

(230−47, 230, 6166)-Net over F₄ — Digital

Digital (183, 230, 6166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−47, 230, 3102814)-Net in Base 4 — Upper bound on s

There is no (183, 230, 3102815)-net in base 4, because

1 times m-reduction [i] would yield (183, 229, 3102815)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744285 940809 144180 840966 217145 613420 812152 147460 757611 691549 860549 000692 663115 385675 180147 052992 239611 207559 234971 562814 429492 881821 057636 > 4²²⁹ [i]