MinT - Best Known (7, 7+55, s)-Nets in Base 256

Best Known (7, 7+55, s)-Nets in Base 256

(7, 7+55, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 62, 264)-net over F₂₅₆, using

net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(7, 7+55, 321)-Net over F₂₅₆ — Digital

Digital (7, 62, 321)-net over F₂₅₆, using

t-expansion [i] based on digital (2, 62, 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]

(7, 7+55, 11809)-Net in Base 256 — Upper bound on s

There is no (7, 62, 11810)-net in base 256, because

1 times m-reduction [i] would yield (7, 61, 11810)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 800 482887 171965 128354 178945 721976 595653 687025 369426 860637 934196 749162 090191 955318 300469 497142 955332 490446 983064 995659 135851 555668 409514 117532 216976 > 256⁶¹ [i]