MinT - Best Known (54−31, 54, s)-Nets in Base 256

Best Known (54−31, 54, s)-Nets in Base 256

(54−31, 54, 522)-Net over F₂₅₆ — Constructive and digital

Digital (23, 54, 522)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (4, 19, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 35, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆ (see above)

(54−31, 54, 1036)-Net over F₂₅₆ — Digital

Digital (23, 54, 1036)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−31, 54, 8134682)-Net in Base 256 — Upper bound on s

There is no (23, 54, 8134683)-net in base 256, because

1 times m-reduction [i] would yield (23, 53, 8134683)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 43 322973 026989 767679 252643 286117 388523 881442 945752 067813 183973 958333 308261 794086 701727 908988 703451 544194 254009 622811 359776 556976 > 256⁵³ [i]