MinT - Best Known (70−30, 70, s)-Nets in Base 4

Best Known (70−30, 70, s)-Nets in Base 4

(70−30, 70, 98)-Net over F₄ — Constructive and digital

Digital (40, 70, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 35, 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]

(70−30, 70, 101)-Net over F₄ — Digital

Digital (40, 70, 101)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−30, 70, 1369)-Net in Base 4 — Upper bound on s

There is no (40, 70, 1370)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 405237 291098 215586 327091 069154 208089 660872 > 4⁷⁰ [i]