MinT - Best Known (88−42, 88, s)-Nets in Base 4

Best Known (88−42, 88, s)-Nets in Base 4

(88−42, 88, 66)-Net over F₄ — Constructive and digital

Digital (46, 88, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 44, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(88−42, 88, 84)-Net over F₄ — Digital

Digital (46, 88, 84)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−42, 88, 947)-Net in Base 4 — Upper bound on s

There is no (46, 88, 948)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 96647 812969 486870 891477 017912 098796 373890 896430 339640 > 4⁸⁸ [i]