MinT - Best Known (231−52, 231, s)-Nets in Base 4

Best Known (231−52, 231, s)-Nets in Base 4

(231−52, 231, 1048)-Net over F₄ — Constructive and digital

Digital (179, 231, 1048)-net over F₄, using

1 times m-reduction [i] based on digital (179, 232, 1048)-net over F₄, using
- trace code for nets [i] based on digital (5, 58, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(231−52, 231, 3555)-Net over F₄ — Digital

Digital (179, 231, 3555)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−52, 231, 785654)-Net in Base 4 — Upper bound on s

There is no (179, 231, 785655)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 908762 923102 683947 391438 762054 299703 432000 246334 965949 840237 755342 300131 876165 426710 552298 493635 705069 939846 795297 796487 131410 180632 795172 > 4²³¹ [i]