MinT - Best Known (246−58, 246, s)-Nets in Base 4

Best Known (246−58, 246, s)-Nets in Base 4

(246−58, 246, 1040)-Net over F₄ — Constructive and digital

Digital (188, 246, 1040)-net over F₄, using

4² times duplication [i] based on digital (186, 244, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 61, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(246−58, 246, 2947)-Net over F₄ — Digital

Digital (188, 246, 2947)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−58, 246, 497862)-Net in Base 4 — Upper bound on s

There is no (188, 246, 497863)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12786 802057 453965 848186 748756 666743 709851 508450 958456 836684 790524 843403 538907 692716 398816 382541 490459 050293 486468 432591 715639 309259 771614 874360 023536 > 4²⁴⁶ [i]