MinT - Best Known (101, 101+49, s)-Nets in Base 4

Best Known (101, 101+49, s)-Nets in Base 4

(101, 101+49, 240)-Net over F₄ — Constructive and digital

Digital (101, 150, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 50, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(101, 101+49, 465)-Net over F₄ — Digital

Digital (101, 150, 465)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+49, 17846)-Net in Base 4 — Upper bound on s

There is no (101, 150, 17847)-net in base 4, because

1 times m-reduction [i] would yield (101, 149, 17847)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509503 611747 495693 645829 966121 134500 526848 352592 648092 076014 373854 605961 672921 495244 837284 > 4¹⁴⁹ [i]