MinT - Best Known (138−45, 138, s)-Nets in Base 4

Best Known (138−45, 138, s)-Nets in Base 4

(138−45, 138, 240)-Net over F₄ — Constructive and digital

Digital (93, 138, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 46, 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]

(138−45, 138, 438)-Net over F₄ — Digital

Digital (93, 138, 438)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−45, 138, 16922)-Net in Base 4 — Upper bound on s

There is no (93, 138, 16923)-net in base 4, because

1 times m-reduction [i] would yield (93, 137, 16923)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30371 193703 116870 477342 171917 914017 632454 454424 067913 477769 329594 778496 363505 756918 > 4¹³⁷ [i]