MinT - Best Known (234−55, 234, s)-Nets in Base 4

Best Known (234−55, 234, s)-Nets in Base 4

(234−55, 234, 1040)-Net over F₄ — Constructive and digital

Digital (179, 234, 1040)-net over F₄, using

4² times duplication [i] based on digital (177, 232, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 58, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(234−55, 234, 2867)-Net over F₄ — Digital

Digital (179, 234, 2867)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−55, 234, 571246)-Net in Base 4 — Upper bound on s

There is no (179, 234, 571247)-net in base 4, because

1 times m-reduction [i] would yield (179, 233, 571247)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 541173 731030 540628 390849 814699 718703 823925 614669 076938 839103 991722 531143 027268 648880 823883 936098 766030 316707 612807 206704 276699 955023 765760 > 4²³³ [i]