MinT - Best Known (5, 5+39, s)-Nets in Base 256

Best Known (5, 5+39, s)-Nets in Base 256

(5, 5+39, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 44, 262)-net over F₂₅₆, using

net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(5, 5+39, 321)-Net over F₂₅₆ — Digital

Digital (5, 44, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 44, 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]

(5, 5+39, 8758)-Net in Base 256 — Upper bound on s

There is no (5, 44, 8759)-net in base 256, because

1 times m-reduction [i] would yield (5, 43, 8759)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 35 838310 483878 191278 024870 660268 934223 154483 506832 955875 623833 144839 884902 143454 467455 289345 712076 040356 > 256⁴³ [i]