MinT - Best Known (151, 222, s)-Nets in Base 4

Best Known (151, 222, s)-Nets in Base 4

(151, 222, 450)-Net over F₄ — Constructive and digital

Digital (151, 222, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 111, 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]

(151, 222, 703)-Net over F₄ — Digital

Digital (151, 222, 703)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 222, 29328)-Net in Base 4 — Upper bound on s

There is no (151, 222, 29329)-net in base 4, because

1 times m-reduction [i] would yield (151, 221, 29329)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 356890 406020 763915 551472 428520 521030 382016 630491 655366 786811 669591 372309 941772 618771 608367 403638 835247 653725 616174 915180 848776 669248 > 4²²¹ [i]