MinT - Best Known (234−77, 234, s)-Nets in Base 4

Best Known (234−77, 234, s)-Nets in Base 4

(234−77, 234, 450)-Net over F₄ — Constructive and digital

Digital (157, 234, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 117, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(234−77, 234, 662)-Net over F₄ — Digital

Digital (157, 234, 662)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−77, 234, 24587)-Net in Base 4 — Upper bound on s

There is no (157, 234, 24588)-net in base 4, because

1 times m-reduction [i] would yield (157, 233, 24588)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 749897 008999 625664 439315 983389 439865 113872 061724 193053 450880 393827 608438 675419 682944 221980 461293 208527 389748 670999 692463 265569 231237 322240 > 4²³³ [i]