MinT - Best Known (106, 153, s)-Nets in Base 4

Best Known (106, 153, s)-Nets in Base 4

(106, 153, 312)-Net over F₄ — Constructive and digital

Digital (106, 153, 312)-net over F₄, using

t-expansion [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, 153, 604)-Net over F₄ — Digital

Digital (106, 153, 604)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 153, 29915)-Net in Base 4 — Upper bound on s

There is no (106, 153, 29916)-net in base 4, because

1 times m-reduction [i] would yield (106, 152, 29916)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 606541 828432 759898 996758 603726 575940 071137 422107 319327 165598 753502 022947 076390 706642 695466 > 4¹⁵² [i]