MinT - Best Known (48−43, 48, s)-Nets in Base 256

Best Known (48−43, 48, s)-Nets in Base 256

(48−43, 48, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 48, 262)-net over F₂₅₆, using

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

(48−43, 48, 321)-Net over F₂₅₆ — Digital

Digital (5, 48, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 48, 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]

(48−43, 48, 8342)-Net in Base 256 — Upper bound on s

There is no (5, 48, 8343)-net in base 256, because

1 times m-reduction [i] would yield (5, 47, 8343)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 154091 754079 065023 769218 706176 808925 335924 343663 038818 329982 815286 228515 665383 451966 118862 910102 847962 220179 818266 > 256⁴⁷ [i]