MinT - Best Known (247−59, 247, s)-Nets in Base 4

Best Known (247−59, 247, s)-Nets in Base 4

(247−59, 247, 1036)-Net over F₄ — Constructive and digital

Digital (188, 247, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (188, 248, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 62, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(247−59, 247, 2771)-Net over F₄ — Digital

Digital (188, 247, 2771)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−59, 247, 497862)-Net in Base 4 — Upper bound on s

There is no (188, 247, 497863)-net in base 4, because

1 times m-reduction [i] would yield (188, 246, 497863)-net in base 4, but
- 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]