MinT - Best Known (106, 154, s)-Nets in Base 4

Best Known (106, 154, s)-Nets in Base 4

(106, 154, 312)-Net over F₄ — Constructive and digital

Digital (106, 154, 312)-net over F₄, using

4¹ times duplication [i] based on digital (105, 153, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 51, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(106, 154, 572)-Net over F₄ — Digital

Digital (106, 154, 572)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 154, 23828)-Net in Base 4 — Upper bound on s

There is no (106, 154, 23829)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 515713 860069 005233 593130 418999 006476 573246 453173 885049 800070 900629 248284 380651 789022 266464 > 4¹⁵⁴ [i]