MinT - Best Known (7, 68, s)-Nets in Base 256

Best Known (7, 68, s)-Nets in Base 256

(7, 68, 264)-Net over F₂₅₆ — Constructive and digital

Digital (7, 68, 264)-net over F₂₅₆, using

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

(7, 68, 321)-Net over F₂₅₆ — Digital

Digital (7, 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]

(7, 68, 11274)-Net in Base 256 — Upper bound on s

There is no (7, 68, 11275)-net in base 256, because

1 times m-reduction [i] would yield (7, 67, 11275)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 225381 540582 016632 875589 051463 000334 918097 969209 348394 028292 779429 984255 835579 837585 573482 381114 237268 500476 771304 248364 491805 064944 840694 671798 608012 105888 069376 > 256⁶⁷ [i]