MinT - Best Known (5, 5+51, s)-Nets in Base 256

Best Known (5, 5+51, s)-Nets in Base 256

(5, 5+51, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 56, 262)-net over F₂₅₆, using

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

(5, 5+51, 321)-Net over F₂₅₆ — Digital

Digital (5, 56, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 56, 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+51, 7916)-Net in Base 256 — Upper bound on s

There is no (5, 56, 7917)-net in base 256, because

1 times m-reduction [i] would yield (5, 55, 7917)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 840853 453208 838607 284202 176745 195750 208291 563395 457257 139638 500245 217072 985937 232365 728210 302594 591861 830384 700471 482369 123933 768376 > 256⁵⁵ [i]