MinT - Best Known (141, 207, s)-Nets in Base 4

Best Known (141, 207, s)-Nets in Base 4

(141, 207, 312)-Net over F₄ — Constructive and digital

Digital (141, 207, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 69, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(141, 207, 670)-Net over F₄ — Digital

Digital (141, 207, 670)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 207, 26202)-Net in Base 4 — Upper bound on s

There is no (141, 207, 26203)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42330 507855 957446 077113 461413 998831 174725 092321 896989 082035 610086 664370 079998 135247 758219 554139 588004 774859 288515 740868 224180 > 4²⁰⁷ [i]