MinT - Best Known (52−47, 52, s)-Nets in Base 256

Best Known (52−47, 52, s)-Nets in Base 256

(52−47, 52, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 52, 262)-net over F₂₅₆, using

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

(52−47, 52, 321)-Net over F₂₅₆ — Digital

Digital (5, 52, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 52, 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]

(52−47, 52, 8078)-Net in Base 256 — Upper bound on s

There is no (5, 52, 8079)-net in base 256, because

1 times m-reduction [i] would yield (5, 51, 8079)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 661 993269 787957 496975 906253 040682 929833 200943 874400 143828 810482 245105 985227 436247 820488 101385 496279 537945 421643 451394 310336 > 256⁵¹ [i]