MinT - Best Known (170−42, 170, s)-Nets in Base 4

Best Known (170−42, 170, s)-Nets in Base 4

(170−42, 170, 1028)-Net over F₄ — Constructive and digital

Digital (128, 170, 1028)-net over F₄, using

4² times duplication [i] based on digital (126, 168, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 42, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(170−42, 170, 1707)-Net over F₄ — Digital

Digital (128, 170, 1707)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−42, 170, 216349)-Net in Base 4 — Upper bound on s

There is no (128, 170, 216350)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 239824 077510 824876 919133 914461 671684 690523 645591 647135 862852 961550 489146 598186 502735 601510 453530 207831 > 4¹⁷⁰ [i]