MinT - Best Known (246−56, 246, s)-Nets in Base 4

Best Known (246−56, 246, s)-Nets in Base 4

(246−56, 246, 1048)-Net over F₄ — Constructive and digital

Digital (190, 246, 1048)-net over F₄, using

4² times duplication [i] based on digital (188, 244, 1048)-net over F₄, using
- trace code for nets [i] based on digital (5, 61, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(246−56, 246, 3534)-Net over F₄ — Digital

Digital (190, 246, 3534)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−56, 246, 733495)-Net in Base 4 — Upper bound on s

There is no (190, 246, 733496)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12787 034489 697652 353197 418158 293093 094161 821138 899789 002468 251083 002478 529639 706529 726140 828166 926425 539456 762254 830142 421703 357410 078073 427967 474524 > 4²⁴⁶ [i]