MinT - Best Known (114−54, 114, s)-Nets in Base 4

Best Known (114−54, 114, s)-Nets in Base 4

(114−54, 114, 76)-Net over F₄ — Constructive and digital

Digital (60, 114, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 57, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(114−54, 114, 106)-Net over F₄ — Digital

Digital (60, 114, 106)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−54, 114, 1246)-Net in Base 4 — Upper bound on s

There is no (60, 114, 1247)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 433 920421 402564 122384 987403 227254 890982 017971 664760 268651 826411 131760 > 4¹¹⁴ [i]