MinT - Best Known (48−42, 48, s)-Nets in Base 256

Best Known (48−42, 48, s)-Nets in Base 256

(48−42, 48, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 48, 263)-net over F₂₅₆, using

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

(48−42, 48, 321)-Net over F₂₅₆ — Digital

Digital (6, 48, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 48, 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]

(48−42, 48, 10866)-Net in Base 256 — Upper bound on s

There is no (6, 48, 10867)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 39 423860 648795 799741 902385 753098 394281 812483 081332 440114 358624 305854 782800 960906 749153 830018 303316 432070 285909 123536 > 256⁴⁸ [i]