MinT - Best Known (50−43, 50, s)-Nets in Base 256

Best Known (50−43, 50, s)-Nets in Base 256

(50−43, 50, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 50, 264)-net over F₂₅₆, using

net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(50−43, 50, 321)-Net over F₂₅₆ — Digital

Digital (7, 50, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 50, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(50−43, 50, 14153)-Net in Base 256 — Upper bound on s

There is no (7, 50, 14154)-net in base 256, because

1 times m-reduction [i] would yield (7, 49, 14154)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 10091 513676 695155 935546 260929 187352 799503 710191 893819 349990 074436 567925 643029 045658 281484 661253 796287 956332 187940 150296 > 256⁴⁹ [i]