MinT - Best Known (154−62, 154, s)-Nets in Base 4

Best Known (154−62, 154, s)-Nets in Base 4

(154−62, 154, 130)-Net over F₄ — Constructive and digital

Digital (92, 154, 130)-net over F₄, using

18 times m-reduction [i] based on digital (92, 172, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 86, 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]

(154−62, 154, 228)-Net over F₄ — Digital

Digital (92, 154, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−62, 154, 4027)-Net in Base 4 — Upper bound on s

There is no (92, 154, 4028)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 522 056597 433688 386178 326978 581313 728020 344298 134292 558702 889707 592498 624595 688761 452396 994040 > 4¹⁵⁴ [i]