MinT - Best Known (230−54, 230, s)-Nets in Base 4

Best Known (230−54, 230, s)-Nets in Base 4

(230−54, 230, 1040)-Net over F₄ — Constructive and digital

Digital (176, 230, 1040)-net over F₄, using

4² times duplication [i] based on digital (174, 228, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 57, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(230−54, 230, 2841)-Net over F₄ — Digital

Digital (176, 230, 2841)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−54, 230, 489694)-Net in Base 4 — Upper bound on s

There is no (176, 230, 489695)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977220 129814 842472 267465 792459 084015 912190 038812 008082 829466 136599 682983 905145 571834 041053 873156 348482 874399 725757 638219 167355 399872 451440 > 4²³⁰ [i]