MinT - Best Known (20, 47, s)-Nets in Base 256

Best Known (20, 47, s)-Nets in Base 256

(20, 47, 521)-Net over F₂₅₆ — Constructive and digital

Digital (20, 47, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 16, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 31, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(20, 47, 947)-Net over F₂₅₆ — Digital

Digital (20, 47, 947)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 47, 7384653)-Net in Base 256 — Upper bound on s

There is no (20, 47, 7384654)-net in base 256, because

1 times m-reduction [i] would yield (20, 46, 7384654)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 601 227210 622159 544143 960052 106813 895983 796352 116038 476278 689028 744428 451958 254258 056943 025423 993447 417724 447511 > 256⁴⁶ [i]