MinT - Best Known (207−68, 207, s)-Nets in Base 4

Best Known (207−68, 207, s)-Nets in Base 4

(207−68, 207, 240)-Net over F₄ — Constructive and digital

Digital (139, 207, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 69, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(207−68, 207, 598)-Net over F₄ — Digital

Digital (139, 207, 598)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−68, 207, 20857)-Net in Base 4 — Upper bound on s

There is no (139, 207, 20858)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42355 466428 900335 874213 844539 085713 818095 131035 362566 330486 531040 559060 342904 028140 622893 261304 898844 392473 468230 355555 228452 > 4²⁰⁷ [i]