MinT - Best Known (180, 180+60, s)-Nets in Base 4

Best Known (180, 180+60, s)-Nets in Base 4

(180, 180+60, 1028)-Net over F₄ — Constructive and digital

Digital (180, 240, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 60, 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]

(180, 180+60, 2169)-Net over F₄ — Digital

Digital (180, 240, 2169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+60, 263091)-Net in Base 4 — Upper bound on s

There is no (180, 240, 263092)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 121907 476972 280129 647525 914678 636545 828369 982052 389668 471008 452882 883426 249194 275946 051814 737163 480280 011576 060406 797670 417869 274861 033933 304424 > 4²⁴⁰ [i]