MinT - Best Known (138−66, 138, s)-Nets in Base 4

Best Known (138−66, 138, s)-Nets in Base 4

(138−66, 138, 76)-Net over F₄ — Constructive and digital

Digital (72, 138, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 69, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(138−66, 138, 120)-Net over F₄ — Digital

Digital (72, 138, 120)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−66, 138, 1418)-Net in Base 4 — Upper bound on s

There is no (72, 138, 1419)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 123017 993613 844570 926949 918910 981990 744554 802729 865918 542361 529319 087687 765447 520712 > 4¹³⁸ [i]