MinT - Best Known (5, 5+63, s)-Nets in Base 256

Best Known (5, 5+63, s)-Nets in Base 256

(5, 5+63, 262)-Net over F₂₅₆ — Constructive and digital

Digital (5, 68, 262)-net over F₂₅₆, using

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

(5, 5+63, 321)-Net over F₂₅₆ — Digital

Digital (5, 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]

(5, 5+63, 7785)-Net in Base 256 — Upper bound on s

There is no (5, 68, 7786)-net in base 256, because

3 times m-reduction [i] would yield (5, 65, 7786)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 438798 165179 430679 543313 138726 391165 741407 484831 552237 186193 384235 680692 673890 504351 277063 345644 404370 612795 817992 395504 540563 478725 949719 204111 632389 753776 > 256⁶⁵ [i]