MinT - Best Known (247−57, 247, s)-Nets in Base 4

Best Known (247−57, 247, s)-Nets in Base 4

(247−57, 247, 1044)-Net over F₄ — Constructive and digital

Digital (190, 247, 1044)-net over F₄, using

1 times m-reduction [i] based on digital (190, 248, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 62, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(247−57, 247, 3301)-Net over F₄ — Digital

Digital (190, 247, 3301)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−57, 247, 733495)-Net in Base 4 — Upper bound on s

There is no (190, 247, 733496)-net in base 4, because

1 times m-reduction [i] would yield (190, 246, 733496)-net in base 4, but
- 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]