MinT - Best Known (245−68, 245, s)-Nets in Base 4

Best Known (245−68, 245, s)-Nets in Base 4

(245−68, 245, 531)-Net over F₄ — Constructive and digital

Digital (177, 245, 531)-net over F₄, using

10 times m-reduction [i] based on digital (177, 255, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 85, 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]

(245−68, 245, 1376)-Net over F₄ — Digital

Digital (177, 245, 1376)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−68, 245, 98311)-Net in Base 4 — Upper bound on s

There is no (177, 245, 98312)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3197 124225 879514 209434 525939 689335 711016 428540 012121 834649 611420 160256 423558 825062 294886 387252 195546 865993 637313 621500 680443 774090 367261 189803 320320 > 4²⁴⁵ [i]