MinT - Best Known (59−55, 59, s)-Nets in Base 256

Best Known (59−55, 59, s)-Nets in Base 256

(59−55, 59, 261)-Net over F₂₅₆ — Constructive and digital

Digital (4, 59, 261)-net over F₂₅₆, using

net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(59−55, 59, 321)-Net over F₂₅₆ — Digital

Digital (4, 59, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 59, 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]

(59−55, 59, 6336)-Net in Base 256 — Upper bound on s

There is no (4, 59, 6337)-net in base 256, because

7 times m-reduction [i] would yield (4, 52, 6337)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 169244 155708 553255 294976 405607 899118 111214 292577 191883 929927 665576 070593 503551 589069 342517 813343 998703 448577 013589 239702 117016 > 256⁵² [i]