MinT - Best Known (66, 126, s)-Nets in Base 4

Best Known (66, 126, s)-Nets in Base 4

(66, 126, 76)-Net over F₄ — Constructive and digital

Digital (66, 126, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 63, 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]

(66, 126, 113)-Net over F₄ — Digital

Digital (66, 126, 113)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 126, 1331)-Net in Base 4 — Upper bound on s

There is no (66, 126, 1332)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7260 265762 957826 169283 870412 615105 457262 907663 610717 678683 603452 259070 960136 > 4¹²⁶ [i]