MinT - Best Known (159, 159+47, s)-Nets in Base 4

Best Known (159, 159+47, s)-Nets in Base 4

(159, 159+47, 1044)-Net over F₄ — Constructive and digital

Digital (159, 206, 1044)-net over F₄, using

4² times duplication [i] based on digital (157, 204, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 51, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(159, 159+47, 3003)-Net over F₄ — Digital

Digital (159, 206, 3003)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+47, 730315)-Net in Base 4 — Upper bound on s

There is no (159, 206, 730316)-net in base 4, because

1 times m-reduction [i] would yield (159, 205, 730316)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 225498 890232 807747 583428 301385 230942 979422 079667 514654 595133 405193 636197 907816 323269 164591 959778 594160 676481 250777 683896 > 4²⁰⁵ [i]