MinT - Best Known (117−38, 117, s)-Nets in Base 4

Best Known (117−38, 117, s)-Nets in Base 4

(117−38, 117, 240)-Net over F₄ — Constructive and digital

Digital (79, 117, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 39, 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]

(117−38, 117, 390)-Net over F₄ — Digital

Digital (79, 117, 390)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−38, 117, 13459)-Net in Base 4 — Upper bound on s

There is no (79, 117, 13460)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27634 773382 502201 703386 526186 887841 145550 967368 623657 752170 735485 706743 > 4¹¹⁷ [i]