MinT - Best Known (5, 58, s)-Nets in Base 256

Best Known (5, 58, s)-Nets in Base 256

(5, 58, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 58, 262)-net over F₂₅₆, using

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

(5, 58, 321)-Net over F₂₅₆ — Digital

Digital (5, 58, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 58, 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, 58, 7864)-Net in Base 256 — Upper bound on s

There is no (5, 58, 7865)-net in base 256, because

1 times m-reduction [i] would yield (5, 57, 7865)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 186494 132529 601888 789045 550754 580349 935430 286938 902004 513733 266797 196322 814008 520196 811772 717369 975082 855336 787180 322057 874490 544638 010576 > 256⁵⁷ [i]