MinT - Best Known (256−58, 256, s)-Nets in Base 4

Best Known (256−58, 256, s)-Nets in Base 4

(256−58, 256, 1052)-Net over F₄ — Constructive and digital

Digital (198, 256, 1052)-net over F₄, using

trace code for nets [i] based on digital (6, 64, 263)-net over F₂₅₆, using
- net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(256−58, 256, 3751)-Net over F₄ — Digital

Digital (198, 256, 3751)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−58, 256, 803016)-Net in Base 4 — Upper bound on s

There is no (198, 256, 803017)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13408 067571 597848 317991 152418 571563 380902 423076 645380 857832 149920 631125 837687 919233 074029 294241 296443 924600 661702 101991 543960 590406 780588 585266 645845 360256 > 4²⁵⁶ [i]