MinT - Best Known (105, 154, s)-Nets in Base 4

Best Known (105, 154, s)-Nets in Base 4

(105, 154, 240)-Net over F₄ — Constructive and digital

Digital (105, 154, 240)-net over F₄, using

2 times m-reduction [i] based on digital (105, 156, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 52, 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]

(105, 154, 526)-Net over F₄ — Digital

Digital (105, 154, 526)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 154, 22490)-Net in Base 4 — Upper bound on s

There is no (105, 154, 22491)-net in base 4, because

1 times m-reduction [i] would yield (105, 153, 22491)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 450223 264869 419705 148442 329157 159735 721930 346595 304445 068179 388094 555464 141311 010790 127329 > 4¹⁵³ [i]