MinT - Best Known (21, 50, s)-Nets in Base 256

Best Known (21, 50, s)-Nets in Base 256

(21, 50, 521)-Net over F₂₅₆ — Constructive and digital

Digital (21, 50, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 17, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 33, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(21, 50, 899)-Net over F₂₅₆ — Digital

Digital (21, 50, 899)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(21, 50, 6364393)-Net in Base 256 — Upper bound on s

There is no (21, 50, 6364394)-net in base 256, because

1 times m-reduction [i] would yield (21, 49, 6364394)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 10086 935483 349151 455196 804441 157281 096941 262624 254754 786166 781280 126340 947221 481336 380635 437641 108424 271446 121392 249456 > 256⁴⁹ [i]