MinT - Best Known (64−59, 64, s)-Nets in Base 256

Best Known (64−59, 64, s)-Nets in Base 256

(64−59, 64, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 64, 262)-net over F₂₅₆, using

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

(64−59, 64, 321)-Net over F₂₅₆ — Digital

Digital (5, 64, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 64, 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]

(64−59, 64, 7789)-Net in Base 256 — Upper bound on s

There is no (5, 64, 7790)-net in base 256, because

1 times m-reduction [i] would yield (5, 63, 7790)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 52 541557 287780 882984 554862 392803 475798 234467 998281 080808 055083 204897 394395 311657 114960 341108 265344 849087 891239 354708 651254 135502 768817 296624 997252 229426 > 256⁶³ [i]