MinT - Best Known (109−34, 109, s)-Nets in Base 4

Best Known (109−34, 109, s)-Nets in Base 4

(109−34, 109, 240)-Net over F₄ — Constructive and digital

Digital (75, 109, 240)-net over F₄, using

2 times m-reduction [i] based on digital (75, 111, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 37, 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]

(109−34, 109, 437)-Net over F₄ — Digital

Digital (75, 109, 437)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−34, 109, 17328)-Net in Base 4 — Upper bound on s

There is no (75, 109, 17329)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 421658 582046 480712 317039 547312 118913 336827 523318 768297 863010 112060 > 4¹⁰⁹ [i]