MinT - Best Known (6, 6+62, s)-Nets in Base 256

Best Known (6, 6+62, s)-Nets in Base 256

(6, 6+62, 263)-Net over F₂₅₆ — Constructive and digital

Digital (6, 68, 263)-net over F₂₅₆, using

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

(6, 6+62, 321)-Net over F₂₅₆ — Digital

Digital (6, 68, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 68, 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+62, 9319)-Net in Base 256 — Upper bound on s

There is no (6, 68, 9320)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 57 734669 086771 833256 227067 366403 401810 489742 602668 207813 399471 505894 378591 847896 876954 092255 049696 585024 586847 254305 570726 045571 310836 302999 342386 614451 948878 081476 > 256⁶⁸ [i]