MinT - Best Known (154, 154+47, s)-Nets in Base 4

Best Known (154, 154+47, s)-Nets in Base 4

(154, 154+47, 1040)-Net over F₄ — Constructive and digital

Digital (154, 201, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (153, 200, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 50, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(154, 154+47, 2586)-Net over F₄ — Digital

Digital (154, 201, 2586)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+47, 540286)-Net in Base 4 — Upper bound on s

There is no (154, 201, 540287)-net in base 4, because

1 times m-reduction [i] would yield (154, 200, 540287)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 582280 648147 725724 454492 320542 055553 786777 202973 926030 017635 418560 794826 752512 939854 257498 895317 789345 546029 842752 753308 > 4²⁰⁰ [i]