MinT - Best Known (98, 98+68, s)-Nets in Base 4

Best Known (98, 98+68, s)-Nets in Base 4

(98, 98+68, 130)-Net over F₄ — Constructive and digital

Digital (98, 166, 130)-net over F₄, using

18 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+68, 230)-Net over F₄ — Digital

Digital (98, 166, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+68, 3897)-Net in Base 4 — Upper bound on s

There is no (98, 166, 3898)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8817 740504 891712 421856 119734 087808 160958 379638 500732 299442 237928 475313 167794 606123 355264 623359 672284 > 4¹⁶⁶ [i]