MinT - Best Known (96, 96+57, s)-Nets in Base 4

Best Known (96, 96+57, s)-Nets in Base 4

(96, 96+57, 130)-Net over F₄ — Constructive and digital

Digital (96, 153, 130)-net over F₄, using

27 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 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]

(96, 96+57, 296)-Net over F₄ — Digital

Digital (96, 153, 296)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+57, 6962)-Net in Base 4 — Upper bound on s

There is no (96, 153, 6963)-net in base 4, because

1 times m-reduction [i] would yield (96, 152, 6963)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 607279 643087 427549 746524 553605 690449 827726 426311 795488 804441 444298 859702 280246 777552 793880 > 4¹⁵² [i]