MinT - Best Known (127, 127+42, s)-Nets in Base 4

Best Known (127, 127+42, s)-Nets in Base 4

(127, 127+42, 1028)-Net over F₄ — Constructive and digital

Digital (127, 169, 1028)-net over F₄, using

4¹ 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]

(127, 127+42, 1651)-Net over F₄ — Digital

Digital (127, 169, 1651)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+42, 202527)-Net in Base 4 — Upper bound on s

There is no (127, 169, 202528)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 559956 736398 026120 168704 970025 687305 364873 505712 538791 358739 820304 997696 052748 608190 382237 466641 786315 > 4¹⁶⁹ [i]