MinT - Best Known (98, 98+78, s)-Nets in Base 4

Best Known (98, 98+78, s)-Nets in Base 4

(98, 98+78, 130)-Net over F₄ — Constructive and digital

Digital (98, 176, 130)-net over F₄, using

8 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, 98+78, 188)-Net over F₄ — Digital

Digital (98, 176, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+78, 2642)-Net in Base 4 — Upper bound on s

There is no (98, 176, 2643)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9180 110826 085101 837640 435310 451062 854697 088711 666922 226421 762880 802546 484978 132358 481516 137172 673982 504000 > 4¹⁷⁶ [i]