MinT - Best Known (170−55, 170, s)-Nets in Base 4

Best Known (170−55, 170, s)-Nets in Base 4

(170−55, 170, 240)-Net over F₄ — Constructive and digital

Digital (115, 170, 240)-net over F₄, using

1 times m-reduction [i] based on digital (115, 171, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 57, 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]

(170−55, 170, 535)-Net over F₄ — Digital

Digital (115, 170, 535)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−55, 170, 21344)-Net in Base 4 — Upper bound on s

There is no (115, 170, 21345)-net in base 4, because

1 times m-reduction [i] would yield (115, 169, 21345)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 560224 572146 678687 889605 695943 700868 059622 675997 006567 573737 467350 558723 022410 681249 451036 132081 578848 > 4¹⁶⁹ [i]