MinT - Best Known (94, 94+80, s)-Nets in Base 4

Best Known (94, 94+80, s)-Nets in Base 4

(94, 94+80, 130)-Net over F₄ — Constructive and digital

Digital (94, 174, 130)-net over F₄, using

2 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 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]

(94, 94+80, 166)-Net over F₄ — Digital

Digital (94, 174, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+80, 2153)-Net in Base 4 — Upper bound on s

There is no (94, 174, 2154)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 581 223295 922646 277549 485686 382215 712141 354474 579220 535104 242074 891716 764140 023737 497244 879183 985648 322863 > 4¹⁷⁴ [i]