MinT - Best Known (136−34, 136, s)-Nets in Base 4

Best Known (136−34, 136, s)-Nets in Base 4

(136−34, 136, 1028)-Net over F₄ — Constructive and digital

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]

(136−34, 136, 1345)-Net over F₄ — Digital

Digital (102, 136, 1345)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−34, 136, 156771)-Net in Base 4 — Upper bound on s

There is no (102, 136, 156772)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7589 285001 346549 136547 417840 666919 609326 150932 153302 072814 699533 991971 703775 775210 > 4¹³⁶ [i]