MinT - Best Known (164−66, 164, s)-Nets in Base 4

Best Known (164−66, 164, s)-Nets in Base 4

(164−66, 164, 130)-Net over F₄ — Constructive and digital

Digital (98, 164, 130)-net over F₄, using

20 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(164−66, 164, 241)-Net over F₄ — Digital

Digital (98, 164, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−66, 164, 4281)-Net in Base 4 — Upper bound on s

There is no (98, 164, 4282)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 550 205103 476814 459592 482113 513888 147410 979544 802160 444093 578492 453005 282386 532194 522477 660048 234017 > 4¹⁶⁴ [i]