MinT - Best Known (74−32, 74, s)-Nets in Base 4

Best Known (74−32, 74, s)-Nets in Base 4

(74−32, 74, 98)-Net over F₄ — Constructive and digital

Digital (42, 74, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 37, 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]

(74−32, 74, 102)-Net over F₄ — Digital

Digital (42, 74, 102)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−32, 74, 1367)-Net in Base 4 — Upper bound on s

There is no (42, 74, 1368)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 359 210205 180944 245695 993208 854268 091424 063985 > 4⁷⁴ [i]