MinT - Best Known (137−34, 137, s)-Nets in Base 4

Best Known (137−34, 137, s)-Nets in Base 4

(137−34, 137, 1028)-Net over F₄ — Constructive and digital

Digital (103, 137, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (102, 136, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 34, 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]

(137−34, 137, 1402)-Net over F₄ — Digital

Digital (103, 137, 1402)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−34, 137, 170092)-Net in Base 4 — Upper bound on s

There is no (103, 137, 170093)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30356 764519 833567 007198 991730 245045 491041 613200 807996 395153 051946 917300 929153 798096 > 4¹³⁷ [i]