MinT - Best Known (122−56, 122, s)-Nets in Base 4

Best Known (122−56, 122, s)-Nets in Base 4

(122−56, 122, 98)-Net over F₄ — Constructive and digital

Digital (66, 122, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 61, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(122−56, 122, 124)-Net over F₄ — Digital

Digital (66, 122, 124)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−56, 122, 1559)-Net in Base 4 — Upper bound on s

There is no (66, 122, 1560)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 739090 475041 287878 680985 055251 973478 728229 595012 452120 694691 209709 677760 > 4¹²² [i]