MinT - Best Known (158, 236, s)-Nets in Base 4

Best Known (158, 236, s)-Nets in Base 4

(158, 236, 450)-Net over F₄ — Constructive and digital

Digital (158, 236, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 118, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(158, 236, 656)-Net over F₄ — Digital

Digital (158, 236, 656)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 236, 22538)-Net in Base 4 — Upper bound on s

There is no (158, 236, 22539)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12207 087065 905316 037358 376198 650012 590391 490717 960508 348524 554289 566168 641479 267167 060286 707680 370179 868889 617294 964163 462598 981670 350196 168704 > 4²³⁶ [i]