MinT - Best Known (54, 54+44, s)-Nets in Base 4

Best Known (54, 54+44, s)-Nets in Base 4

(54, 54+44, 98)-Net over F₄ — Constructive and digital

Digital (54, 98, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 49, 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]

(54, 54+44, 111)-Net over F₄ — Digital

Digital (54, 98, 111)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+44, 1433)-Net in Base 4 — Upper bound on s

There is no (54, 98, 1434)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 101745 844407 921018 373275 333525 030042 817646 222528 414570 227180 > 4⁹⁸ [i]