MinT - Best Known (184−86, 184, s)-Nets in Base 4

Best Known (184−86, 184, s)-Nets in Base 4

(184−86, 184, 130)-Net over F₄ — Constructive and digital

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]

(184−86, 184, 165)-Net over F₄ — Digital

Digital (98, 184, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−86, 184, 2086)-Net in Base 4 — Upper bound on s

There is no (98, 184, 2087)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 611 063003 625136 019328 091712 840631 613664 158064 904494 804922 962569 066108 099441 814230 357584 126328 228299 484294 205440 > 4¹⁸⁴ [i]