MinT - Best Known (98−40, 98, s)-Nets in Base 4

Best Known (98−40, 98, s)-Nets in Base 4

(98−40, 98, 130)-Net over F₄ — Constructive and digital

Digital (58, 98, 130)-net over F₄, using

6 times m-reduction [i] based on digital (58, 104, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 52, 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]

(98−40, 98, 152)-Net over F₄ — Digital

Digital (58, 98, 152)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−40, 98, 2451)-Net in Base 4 — Upper bound on s

There is no (58, 98, 2452)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 100843 174039 259153 679055 489318 220563 086706 523827 428273 932656 > 4⁹⁸ [i]