MinT - Best Known (204−50, 204, s)-Nets in Base 4

Best Known (204−50, 204, s)-Nets in Base 4

(204−50, 204, 1032)-Net over F₄ — Constructive and digital

Digital (154, 204, 1032)-net over F₄, using

trace code for nets [i] based on digital (1, 51, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(204−50, 204, 2069)-Net over F₄ — Digital

Digital (154, 204, 2069)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−50, 204, 277512)-Net in Base 4 — Upper bound on s

There is no (154, 204, 277513)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 095898 056984 518471 889663 206907 451725 113202 156465 186266 622905 844369 074373 849083 037448 156506 885899 032059 458060 777464 632064 > 4²⁰⁴ [i]