MinT - Best Known (5, 36, s)-Nets in Base 256

Best Known (5, 36, s)-Nets in Base 256

(5, 36, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 36, 262)-net over F₂₅₆, using

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

(5, 36, 321)-Net over F₂₅₆ — Digital

Digital (5, 36, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 36, 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, 36, 10475)-Net in Base 256 — Upper bound on s

There is no (5, 36, 10476)-net in base 256, because

1 times m-reduction [i] would yield (5, 35, 10476)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 1 945014 570159 665763 926221 537900 541452 236337 396671 535082 827919 306494 544145 300710 539576 > 256³⁵ [i]