MinT - Best Known (156, 156+52, s)-Nets in Base 4

Best Known (156, 156+52, s)-Nets in Base 4

(156, 156+52, 1028)-Net over F₄ — Constructive and digital

Digital (156, 208, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 52, 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]

(156, 156+52, 1914)-Net over F₄ — Digital

Digital (156, 208, 1914)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+52, 230468)-Net in Base 4 — Upper bound on s

There is no (156, 208, 230469)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169237 269519 308456 718145 978635 202948 836151 346277 233850 329842 115391 916816 837862 394466 162373 901211 744132 943091 806210 284547 453104 > 4²⁰⁸ [i]