MinT - Best Known (115, 115+38, s)-Nets in Base 4

Best Known (115, 115+38, s)-Nets in Base 4

(115, 115+38, 1028)-Net over F₄ — Constructive and digital

Digital (115, 153, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (114, 152, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 38, 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]

(115, 115+38, 1526)-Net over F₄ — Digital

Digital (115, 153, 1526)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+38, 186305)-Net in Base 4 — Upper bound on s

There is no (115, 153, 186306)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 376188 741490 982727 330339 194655 027352 591200 037187 313869 155944 361363 481472 960909 529904 631648 > 4¹⁵³ [i]