MinT - Best Known (242−75, 242, s)-Nets in Base 4

Best Known (242−75, 242, s)-Nets in Base 4

(242−75, 242, 450)-Net over F₄ — Constructive and digital

Digital (167, 242, 450)-net over F₄, using

12 times m-reduction [i] based on digital (167, 254, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 127, 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]

(242−75, 242, 857)-Net over F₄ — Digital

Digital (167, 242, 857)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−75, 242, 40737)-Net in Base 4 — Upper bound on s

There is no (167, 242, 40738)-net in base 4, because

1 times m-reduction [i] would yield (167, 241, 40738)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 493829 016025 287490 992130 522897 002901 572120 276657 358283 414469 781642 128154 510532 939426 550768 850343 560755 592479 300432 344160 879152 156075 495319 438784 > 4²⁴¹ [i]