MinT - Best Known (6, 6+59, s)-Nets in Base 256

Best Known (6, 6+59, s)-Nets in Base 256

(6, 6+59, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 65, 263)-net over F₂₅₆, using

net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(6, 6+59, 321)-Net over F₂₅₆ — Digital

Digital (6, 65, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 65, 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]

(6, 6+59, 9433)-Net in Base 256 — Upper bound on s

There is no (6, 65, 9434)-net in base 256, because

1 times m-reduction [i] would yield (6, 64, 9434)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 13431 654190 274904 017982 530868 486126 411099 364210 607055 437098 327523 086852 004354 542195 375319 047296 834429 374590 722652 013832 716843 357642 431215 279766 720793 303056 > 256⁶⁴ [i]