MinT - Best Known (155−61, 155, s)-Nets in Base 4

Best Known (155−61, 155, s)-Nets in Base 4

(155−61, 155, 130)-Net over F₄ — Constructive and digital

Digital (94, 155, 130)-net over F₄, using

21 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(155−61, 155, 248)-Net over F₄ — Digital

Digital (94, 155, 248)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−61, 155, 4921)-Net in Base 4 — Upper bound on s

There is no (94, 155, 4922)-net in base 4, because

1 times m-reduction [i] would yield (94, 154, 4922)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 523 353816 880488 182473 494301 783296 001602 320475 343998 065315 951769 843970 337647 804829 274374 908912 > 4¹⁵⁴ [i]