MinT - Best Known (98, 170, s)-Nets in Base 4

Best Known (98, 170, s)-Nets in Base 4

(98, 170, 130)-Net over F₄ — Constructive and digital

Digital (98, 170, 130)-net over F₄, using

14 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]

(98, 170, 211)-Net over F₄ — Digital

Digital (98, 170, 211)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 170, 3287)-Net in Base 4 — Upper bound on s

There is no (98, 170, 3288)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 262306 101888 038566 226556 586408 546406 880563 984455 477480 451961 573219 980539 274691 481779 963577 864733 412890 > 4¹⁷⁰ [i]