MinT - Best Known (246−55, 246, s)-Nets in Base 4

Best Known (246−55, 246, s)-Nets in Base 4

(246−55, 246, 1052)-Net over F₄ — Constructive and digital

Digital (191, 246, 1052)-net over F₄, using

4² times duplication [i] based on digital (189, 244, 1052)-net over F₄, using
- trace code for nets [i] based on digital (6, 61, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(246−55, 246, 3892)-Net over F₄ — Digital

Digital (191, 246, 3892)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−55, 246, 1057824)-Net in Base 4 — Upper bound on s

There is no (191, 246, 1057825)-net in base 4, because

1 times m-reduction [i] would yield (191, 245, 1057825)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3196 747034 381889 103577 890493 975550 680331 507930 180102 708936 066077 990993 726539 865293 658685 290435 230893 215584 820331 820808 395054 633171 727521 025385 888160 > 4²⁴⁵ [i]