MinT - Best Known (12−10, 12, s)-Nets in Base 256

Best Known (12−10, 12, s)-Nets in Base 256

(12−10, 12, 259)-Net over F₂₅₆ — Constructive and digital

Digital (2, 12, 259)-net over F₂₅₆, using

net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(12−10, 12, 321)-Net over F₂₅₆ — Digital

Digital (2, 12, 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]

(12−10, 12, 6150)-Net in Base 256 — Upper bound on s

There is no (2, 12, 6151)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 79243 033390 275441 430519 244026 > 256¹² [i]